The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

Lithium batteries are widely used due to their advantages such as high energy density, stable performance, low pollution, and long recyclable life. Accurate SOC estimation is important for the use of lithium batteries. To address the problem of low accuracy of SOC estimation by traditional methods, this paper proposes a joint method of fractional order robust unscented Kalman filter (FORUKF) and robust unscented Kalman filter (RUKF) to estimate SOC. The method is based on a fractional order model (FOM) that combines the unscented transformation (UT) technique, the H∞ observer and the joint estimator. Specifically, an adaptive genetic algorithm (AGA) was first used to identify the parameters of the FOM for lithium batteries and to verify the accuracy of the model. Estimation and updating of the ohmic resistance R0 and the capacity QN in the model in real-time by RUKF and then estimation of the SOC by FORUKF. Finally, the accuracy of FORUKF-RUKF was verified under the Federal Urban Driving Schedule (FUDS), US06 Highway Driving Schedule and Beijing Dynamic Stress Test (BJDST). According to the results, the FORUKF-RUKF estimated SOC was found to have better accuracy and robustness than the RUKF, FOUKF and EKF.

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

In order to overcome the limitation of the traditional adaptive Unscented Kalman Filtering (UKF) algorithm in noise covariance estimation for statement and measurement, we propose a hybrid adaptive UKF algorithm based on combining Maximum a posteriori (MAP) criterion and Maximum likelihood (ML) criterion, in this paper. First, to prevent the actual noise covariance deviating from the true value which can lead to the state estimation error and arouse the filtering divergence, a real-time covariance matrices estimation algorithm based on hybrid MAP and ML is proposed for obtaining the statement and measurement noises covariance, respectively; and then, a balance equation the two kinds of covariance matrix is structured in this proposed to minimize the statement estimation error. Compared with the UFK based MAP and based ML, the proposed algorithm provides better convergence and stability.

This paper aims to demonstrate that, beyond the small world of Riemann-Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to the different paths taken. Notions of time and scale sequences are introduced and general associated basic derivatives, namely right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to get both known and new fractional order derivatives. Several fractional derivatives are considered, mainly: Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.

This article aims to explore the existence and stability of solutions to differential equations involving a regularized ψ−Hilfer fractional derivative, which, compared to standard ψ−Hilfer fractional derivatives, provide a clear physical interpretation when dealing with initial conditions. We discovered that the regularized ψ−Hilfer fractional derivative can be represented as the inverse operation of the ψ−Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a regularized ψ−Hilfer fractional derivative. Additionally, we applied the Mönch’s fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a regularized ψ−Hilfer fractional derivative, and further discussed Ulam-Hyers-Rassias stability and semi-Ulam-Hyers-Rassias stability of these solutions. Finally, we illustrated our results through case studies.

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

The severe climate changes due to global warming pushed the world to strive to reduce carbon emissions. This study aims to minimize the carbon emissions for a proposed smart energy hub. This paper prioritizes the minimization of carbon emissions, taking into consideration the minimization of operation running costs, and the maximization of profit. In this paper two optimization scenarios were studied, to compare the results. In the first scenario, the minimization of carbon emissions was achieved, in the second scenario, the minimization of running costs and maximization of profit from the hub assets were studied. The proposed model was designed in MATLAB. Then the results were verified by CPLEX and validated by RTDS. The multi-objective model was presented to obtain the optimal operation. The mitigation of data uncertainty was achieved by applying the Kalman filter. In this work, a novel method was proposed for the estimation of the quarter-hour resolution data from the hourly one via the Kalman filter rather than applying the classic polynomial interpolation methods.

Dried blood spot (DBS) testing on confetti is one of the most common methods used to collect and extract DNA from field samples for molecular epidemiology of malaria studies. Here, we investigated whether ethanol or other solutions used to clean scissors are a source of sample contamination. DBS were prepared from 3 drops of blood from two Plasmodium falciparum cultures spotted on confetti, and 3 solutions (water, ethanol and DNase) were used to clean scissors between spots during DNA extraction. For each cleaning solution, two blank confetti were used as negative controls. Samples were analyzed by PCR-based genotyping of merozoite surface proteins 1 & 2 (msp-1 and msp-2), and P. falciparum chloroquine resistance transporter (Pfcrt). A total of 15 samples were analyzed. Based on msp-1 and msp-2 amplification, P. falciparum was detected on blank confetti when scissors were washed with ethanol. Based on Pfcrt amplification, DNA of P. falciparum was detected on blank confetti when scissors were cleaned with ethanol or water. No P. falciparum genes were detected on blank confetti when scissors were cleaned with DNase. Scissors cleaned with DNase prevented cross-contamination between samples during processing of dried blood spots, whereas ethanol (which is commonly used) fails to avert cross-contamination.

In this paper the one-to-one correspondences and equivalences between ideals, primals, filters and grills are introduced. It is shown the local functions and the topological spaces induced by them are the same. From this point of view, the topological properties with respect to one topology can be derived from topological properties valid in the corresponding topology.

High-precision ground point cloud data has a wide range of applications in various fields, and the separation of ground points from non-ground points is a crucial preprocessing step. Therefore, designing an efficient, accurate, and stable ground extraction algorithm is of great significance for improving the processing efficiency and analysis accuracy of point cloud data. The study area in this article was a Park in Guilin, Guangxi, China. The point cloud was obtained by utilizing the UAV platform. In order to improve the stability and accuracy of the Filter algorithm, this article proposed a triangular grid filter based on Slope Filter, found violation points by the spatial position relationship within each point in the triangulation network, improved KD-Tree-Based Euclidean Clustering, and applied it to the non-ground points extraction, this method has good accuracy, stability and achieves good results in separating ground points from non-ground points. At first, using Slope Filter to remove some non-ground points, to reduce the error of taking ground points as non-ground points; Secondly, established a triangular grid based on the triangular relationship between each point, the violation-triangle can determin through the grid, and then the corresponding violation points were found in the violation-triangle; Thirdly, according to the three-point collinear method to extract the regular points, used these points to extract the regular landmarks by KD-Tree-Based Euclidean Clustering and Convex Hull Algorithm; Finally, removed disperse points and irregular landmarks by Clustering Algorithm. In order to confirm the superiority of this algorithm, this article compared the filter effects of various algorithms on the study area and filtered the 15 sample data provided by ISPRS, and obtained an average error of 3. 46%. The results showed that the algorithm in this article have a high processing efficiency and accuracy, which can greatly improve the processing efficiency of point cloud data in practical applications.

A time-sequential working, spatially multiplexed autostereoscopic 3D display design consisting of a fast switchable RGB-color filter array is presented. The wavelength-selective filter barrier emits the light from a display over a larger active area than common autostereoscopic barrier displays. An optical modelling of wavelength-selective barriers has been used for instance to calculate the light ray distribution properties of that arrangement. To find well working display designs, automated searches by simulation and computational evaluation has been proceeded. Wavelength-selective filter barrier arrangements exhibit characteristics different from common barrier displays with similar barrier pitch and ascent. In particular, these constructions show strong angular luminance dependency under barrier inclination specified by correspondent slant angle. In time-sequential implementation it is important to avoid that quick eye or eyelid movement lead to visible color artifacts. In the millisecond regime tunable liquid crystal Fabry-Pérot color filters for the colors red, green and blue are presented. They consist of a sub-micrometer thick nematic layer sandwiched between dielectric mirrors and ITO-electrodes. These cells shall switch narrow-banding light of red, green or blue. An array for a glasses-free 3D display has to be equipped with several thousand switchable filter elements having different color apertures. The newly introduced design is usable as a multi user display as well as a single user system with user adaptive control.

We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.

To address the issue of reduced orbit estimation accuracy resulting from discrepancies between in-orbit measured geomagnetic field values and IGRF model values in autonomous orbit estimation of microsatellites based on geomagnetic field measurements, this study introduces an adaptive cubature H-infinity filtering algorithm. Firstly, it presents the low-altitude orbital dynamics model and geomagnetic field measurement model for microsatellites. Subsequently, within the adaptive cubature H-infinity filtering algorithm, a spherical simplex rule and a second-order Gaussian-Legendre quadrature criterion are employed to compute the spherical surface integral and radial integral. Additionally, a spherical simplex-radial quadrature rule is proposed to enhance the approximation accuracy of nonlinear Gaussian weighted integrals. Furthermore, by integrating extended H-infinity filtering based on game theory with the cubature quadrature rule, an inverse proportional relationship between constraint level and filtering innovation is established. This allows for adaptive adjustment of the constraint level to enhance robustness against model errors. Finally, through semi-physical simulation experiments, it is demonstrated that compared with traditional algorithms, the proposed algorithm improves autonomous orbit estimation position accuracy of microsatellites by 7.49%, while also enhancing velocity accuracy by 3.1%, thus validating its effectiveness.

In this paper, we consider the Cauchy problem of a time fractional nonlinear diffusion equation. According to the Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time for some sufficient conditions. We next give sufficient conditions for the existence of global solutions by using the result of Zhang and Sun. In conclusions, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

With the growing demand for positioning services, angle-of-arrival (AoA) estimation or direction-finding (DF) has been widely investigated for applications in fifth-generation (5G) technologies. Many existing AoA estimation algorithms only require the measurement of the direction of the incident wave at the transmitter to obtain correct results. However, for most of the cellular systems such as Bluetooth indoor positioning system due to multipath and non-line-of-sight (NLOS) propagation, the indoor positioning accuracy is severely affected. In this paper a comprehensive algorithm is investigated that combines radio measurements from Bluetooth AoA local navigation systems with indoor position estimates obtained using particle filtering, which allows us to explore new optimised methods to reduce estimation errors in indoor positioning. First, particle filtering is used to predict the rough position of a moving target. Then, an algorithm with robust beam weighting is used to estimate the AoA of the multipath components. Based on this, a system of pseudo-linear equations for target positioning based on the probabilistic framework of PF and AoA measurement is derived. Theoretical analysis and simulation results show that the algorithm can improve the positioning accuracy by about 25.7% on average.

Artificial neural networks are highly efficient tools for numerous kinds of tasks, which include forecasting, regression, and recognizing patterns in classification and pattern recognition. An artificial neural network is a model for processing information using essential components called artificial neurons that are inspired by the human brain. Two significant aspects of delayed neural networks dynamic activity are their stability and the synchronization phenomenon. This work presents a bidirectional associative memory (BAM) incommensurate fractional-order delay neural network model. The incommensurate fractional orders are calculated within the stability region through the corresponding eigenvalues and their points of equilibrium. The involved neuron states are synchronized with each other for the calculated incommensurate stable fractional orders. The reduction of the time delay will give more relaxation time for the state variable $w_4(t)$ to be stable as compared to the state variable $w_3(t)$ due to the induction of extra activation functions. The theoretical findings of this research have significance for providing guidance and controlling the dynamic behavior of artificial neural networks.

In traditional finance, option prices are typically calculated using crisp sets of variables. However, in a proposed new approach, the assumption is made that these parameters have a degree of fuzziness or uncertainty associated with them. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. To determine the belief degree associated with a particular option price, an interpolation search algorithm was proposed recently[1]. Interpolation is a mathematical technique used to estimate values between known data points. In this case, the algorithm is applied to determine the belief degree associated with a specific option price within the range of possible prices. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. It allows them to consider their risk preferences and beliefs about the uncertain parameters when selecting an option price. In this paper, we will review a unified framework for combining fractional Brownian motion with fuzzy processes and obtain a joint measure space. We start by constructing a product measure space that captures the randomness and fuzziness inherent in the respective processes. We begin with the usual Kolmogorov filtered probability space (Ω, F, ℙ), where ℙ represents the probability measure, Ω is the set of all possible outcomes or states that a random process can take and {Ft, t ∈ [0, T]} is an information filtration. We will review the work of Merton (1976) on option pricing when the underlying stock returns have jumps [2] and expand it to fuzzy fractional processes.

In this paper, we extend the KdVSKR equations in (1+1)-dimension and (2+1)-dimension to fractional KdVSKR equations with modified Riemann-Liouville derivative. The (2+1)-dimensional KdVSKR equation, which is a recent extension of (1+1)-dimensional KdVSKR equation, can model the resonances of solitons in shallow water. By means of the Hirota bilinear method, finite symmetry group method and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton-cnoidal interaction solution of the (1+1)-dimensional fractional KdVSKR equation has been derived for the first time. For the (2+1)-dimensional frac-tional KdVSKR equation, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. Impact of the fractional order on the shapes of these solutions has been illustrated by figures. Three-wave interaction solutions of fractional systems have not been reported in the existing references. The research idea in this paper can be applied to other fractional differential equations.

We consider fractional integral operators $(I-T)^d, d \in (-1,1)$ acting on functions $g: \mathbb{Z}^{\nu} \to \mathbb{R}, \nu \ge 1 $, where $T $ is the transition operator of a random walk on $\mathbb{Z}^{\nu}$. We obtain sufficient and necessary conditions for the existence, invertibility and square summability of kernels $\tau (\mathbf{s}; d), \mathmb{s} \in \mathbb{Z}^{\nu}$ of $(I-T)^d $. Asymptotic behavior of $\tau (\mathbf{s}; d)$ as $|\mathbf{s}| \to \infty$ is identified following local limit theorem for random walk. A class of fractionally integrated random fields $X$ on $\mathbb{Z}^{\nu}$ solving the difference equation $(I-T)^d X = \varepsilon$ with white noise on the right-hand side is discussed, and their scaling limits. Several examples including fractional lattice Laplace and heat operators are studied in detail.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning & fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

Fractional flow reserve (FFR) is regarded as the gold standard for assessing the functional significance of coronary artery lesions, yet it remains underutilized in clinical practice. Our objective was to investigate whether FFR results have the potential to alter treatment decisions for coronary lesions compared to visual assessments of angiographic images made by three operators at a high-volume interventional center. In this retrospective study, we aimed to reassess the angiographic images of 63 patients presenting with chronic coronary syndrome (n=39, 61.9%) and acute coronary syndrome (n=24, 38.1%) who underwent FFR. Three experienced interventional cardiologists (with >300 PCI procedures per year) reevaluated, blinded to FFR results, 105 ambiguous lesions in 63 patients to determine angiographic significance and treatment strategy. The observers reached a concordant agreement (≥2 operators made the same decision) to perform PCI in 60 (57.1%) of the lesions based on angiographic evaluation. Interestingly, 9 (15%) of these lesions were functionally non-significant (FFR >0.80). The observers agreed to defer PCI in 45 (42.9%) of the lesions; however, 4 (8.9%) of these were functionally significant (FFR ≤0.80) and required PCI. Thus, inter-observer concordance in visual-guided therapeutic decision-making is variable and not always confirmed by the functional significance of coronary lesions.

Quadruped robots possess significant mobility in complex and uneven terrains due to their outstanding stability and flexibility, making them highly suitable in rescue missions, environmental monitoring, and smart agriculture. With the increasing use of quadruped robots in more demanding scenarios, ensuring accurate and stable state estimation in complex environments has become particularly important. Existing state estimation algorithms relying on multi-sensor fusion, such as those using IMU, LiDAR, and visual data, often face challenges on non-stationary terrains due to issues like foot-end slippage or unstable contact, leading to significant state drift. To tackle this problem, this paper introduces a state estimation algorithm that integrates an Invariant Extended Kalman Filter (InEKF) with a disturbance observer, aiming at estimating the motion state of quadruped robots on non-stationary terrains. Firstly, foot-end slippage is modeled as a deviation in body velocity and explicitly included in the state equations, allowing for a more precise representation of how slippage affects the state. Secondly, the state update process integrates both foot-end velocity and position observations to improve the overall accuracy and comprehensiveness of the estimation. Lastly, a foot-end contact probability model, coupled with an adaptive covariance adjustment strategy, is employed to dynamically modulate the influence of the observations. These enhancements significantly improve the filter's robustness and the accuracy of state estimation in non-stationary terrain scenarios. Experiments conducted with the Jueying Mini quadruped robot on various non-stationary terrains show that the enhanced InEKF method offers notable advantages over traditional filters in compensating for foot-end slippage and adapting to different terrains.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems.

The advancement of technology and the availability of specialized digital signal processing chips have made digital filter design and implementation more feasible in a variety of fields, including biomedical engineering. This paper makes two key contributions. First, it uses a genetic algorithm to optimize the coefficients of Finite Impulse Response (FIR) filters. Second, it conducts a case study on using genetic algorithms to optimize FIR filters for electrocardiogram (ECG) biomedical signal noise removal. The goal of the proposed filter design approach is to achieve the desired signal bandwidth while minimizing the side lobe level and eliminating unwanted signals using a genetic algorithm. The results of the comprehensive analysis of the impact of different genetic operators show that the genetic algorithm-based filter outperforms conventional filter designs.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

Due to its potential harm to space payload, microwave corona breakdown of microstrip circuits has attracted much attention. This work describes an efficient way to suppress corona breakdown. Since corona breakdown threshold is determined by the highest electric field intensity at the surface of microstrip circuits, lacquer coating with thickness of tens of microns is sprayed on the top of microstrip circuits. The applied dielectric coating is used to move the discharge location away from circuit’s surface which is equivalent to reduce the highest electric field intensity on the in-terface of solid/air of the circuit and thus results into higher breakdown threshold. Two designs of classic coupled-line band-pass filter were used for verification. Corona experimental results at 2.5 GHz show that, in the interested low pressure range (100 to 4500 Pa), 5.3 dB improvement of mi-crowave corona breakdown threshold can be achieved for a filter with narrowest gap of 0.2 mm while its electrical performances like insertion loss, Q-factor are still acceptable. A threshold improvement prediction method is also presented and validated.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

Chronic Obstructive Pulmonary Disease (COPD) is a disease characterized by local and systemic inflammation independently of the risk factor; during the exacerbations, such inflammation is accentuated and amplified. A practical inflammatory marker and one with an applicable predictive value in the follow-up has been sought. FeNO has shown an excellent performance in that respect within the context of asthma and has also been studied in tobacco-smoke COPD (COPD-TS). In Biomass-smoke COPD (COPD-BS), this, to our knowledge, has not been evaluated. Objective: To measure FeNO levels in patients with COPD-BS and to compare these with those of patients with stable COPD-TS and in healthy controls. Methods: Transversal, observational, descriptive, comparative, and analytical study. A total of 57 patients, including 23 with COPD-BS, 17 with COPD-TS, and 17 healthy control subjects. The measurement of FeNO was carried out on all of these by means of the on-line chemiluminescence technique; the values were expressed in parts per billion (ppb) for their analysis. Results: It was observed that the FeNO values were similar between COPD-BS and COPD-TS and were significantly different between the healthy and stable COPD (both groups). No correlation was found between pulmonary function and symptoms with FeNO in any of the groups. Conclusions: The level of FeNO in stable COPD is found to be increased in a similar manner in COPD-BS and COPD-TS, with a significant difference on comparing it with that of the healthy subjects.

Snow cover products are primarily derived from the Moderate-resolution Imaging Spectrometer (MODIS) and Advanced Very High-Resolution Radiometer (AVHRR) datasets. MODIS achieves both snow/non-snow discrimination and snow cover fractional retrieval, while early AVHRR-based snow cover products only focused on snow/non-snow discrimination. The AVHRR Climate Data Record (AVHRR -CDR) provides a nearly 40-year global dataset that has a potential to fill a gap in long term snow cover fractional monitoring. Our study selects the Qinghai-Tibet Plateau as the experimental area, utilizing AVHRR-CDR surface reflectance data (AVH09C1) and calibrating with MODIS snow product MOD10A1. The snow cover percentage retrieval from the AVHRR dataset is performed using Surface reflectance at 0.64μm (SR1) and Surface reflectance at 0.86μm (SR2), along with a simulated Normalized Difference Snow Index (NDSI) model. Also, in order to detect the effects of land cover type and topography on snow inversion, we tested the accuracy of the algorithm with and without these influences, respectively (vanilla algorithm & improved algorithm). The accuracy of the AVHRR snow cover percentage data product is evaluated using MOD10A1、 ground snow-depth measurements and ERA5. Results indicate that the logic model based on NDSI has the best fitting effect, with R-square and RMSE values of 0.83 and 0.10, respectively. Meanwhile, the accuracy was improved after taking into account the effects of land cover type and topography. The model is validated using MOD10A1 snow-covered areas, showing snow cover area differences of less than 4% across 6 temporal phases. Improved algorithm results in better consistency with MOD10A1 than vanilla algorithm. Moreover, the RMSE reaches greater levels when the elevation is below 2,000 meters or above 6,000 meters, and is lower when the slope is between 16° and 20°. Using ground snow-depth measurements as ground truth, the multi-year recall rates are mostly above 0.7, with an average recall rate of 0.81. Results also show a high degree of consistency with ERA5. The validation results demonstrate that the AVHRR snow cover percentage remote sensing product proposed in this study exhibits high accuracy in the Tibetan Plateau region, also demonstrating that land cover type and topographic factors are important to the algorithm. Our study lays the foundation for the global snow cover percentage product based on AVHRR-CDR，furthermore lays a basic work for generating a long-term AVHRR-MODIS fractional snow cover dataset.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of dual-phase-lag heat conduction model with the Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag-Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

Neural-objective and image optimization approaches for drilling fluid rheology automation are crucial for drilling engineering optimization. A myriad of intelligent computational models are employed to predict and monitor the parameters of mud rheology and filter cake permeability posture using an artificial neural network feedforward (ANN-FF) function, a non-ANN-FF function, an image processing tool, and a model optimization tool. 498 datasets of synthetic-based mud (SBM) flat rheology from a drilling mud laboratory at Nazarbayev University were imported into a user-friendly MATLAB application using image processing and nftool. Apart from the Google TensorFlow Sequential API DNN architecture used, a Levenberg-Marquardt training algorithm with input sigmoid hidden neurons 10, 12, and 18 coupled with a linear output layer was also used to predict the SBM flow index. OBM and SBM filter cakes were processed for void spaces; however, a model study was extrapolated to maximize filtration volume Vf. The study’s findings show that the ANN-FF model employed for rheological property monitoring and prediction had higher steady and exponential levels of accuracy and a correlation coefficient of 0.96-0.99. More so, SBM and OBM image processing presented an area of void spaces of 1790M2 and 1739M2, respectively. The porosity and permeability postures of both SBM and OBM resulted in a significant void space capable of maximizing the flow index. In addition, the single-objective modelling based on a genetic algorithm did validate the experimental rheological data for flow index or filtration volume Vf optimization; the study resulted in the finding that the constrained physics-informed objective function hindered maximizing oil recovery and instead predicted possible formation damage. It is empirical to note that automating flow predictions with neural, objective, and image functions has presented an alternative novel method for non-programmers using MATLAB and Google Colabs that is capable of enhancing mud rheological parameters, drilling efficiency, and hydrocarbon recovery.

Guided image filter implicitly balances noise and details based on local variance, achieving noise suppression while preserving prominent edges. However, we have observed limitations in using variance to distinguish between noise and image details, resulting in the suppression of fine structures alongside noise. Furthermore, the goal of enhancing image details, which is crucial in image filtering, has not been adequately addressed in edge-preserving filter design. In this paper, we approach image filtering as a problem of spectral energy reconfiguration, where the gain of each spectral band is adaptively regulated to achieve simultaneous noise suppression and detail enhancement. Instead of relying on variance, we employ a linear noise estimator to obtain the Signal-to-Noise Ratio (SNR) measurement necessary for dynamic gain regulation. Similar to the guided image filter, we determine the filter coefficients by solving the closed-form solution of the optimizer. We demonstrate that the proposed extended guided filter effectively integrates information from multiple spectral bands locally, allowing for the joint enhancement of meaningful details while simultaneously smoothing noise.

Face detection is an important problem in computer vision because it enables a wide range of applications, such as facial recognition and analysis of human behavior. The problem is challenging because of the large variations in facial appearance across different individuals and different lighting and pose conditions. One way to detect faces is to utilize a highly advanced face detection method, such as RetinaFace, which uses deep learning techniques to achieve high accuracy in various datasets. However, even the best face detectors can produce false positives, which can lead to incorrect or unreliable results. In this paper, we propose a method for reducing false positives in face detection by using information from a depth map. A depth map is a two-dimensional representation of the distance of objects in an image from the camera. By using the depth information, the proposed method is able to better differentiate between true faces and false positives. The authors evaluate their method on a combined dataset of 549 images, containing a total of 614 upright frontal faces. The results show that the proposed method is able to significantly reduce the number of false positives without sacrificing the overall detection rate. This indicates that the use of depth information can be a useful tool for improving face detection performance.

Traditional computer vision techniques aim to extract meaningful information from images but often depend on manual feature engineering, making it difficult to handle complex real-world scenarios. Fractional Calculus (FC), which extends derivatives to non-integer orders, provides a flexible way to model systems with memory effects and long-term dependencies, making it a powerful tool for capturing fractional rates of variation. Recently, Neural Networks (NNs) have demonstrated remarkable capabilities in learning complex patterns directly from raw data, automating computer vision tasks and enhancing performance. Therefore, the use of fractional calculus in neural network-based computer vision is a powerful method to address existing challenges by effectively capturing complex spatial and temporal relationships in images and videos. This paper presents a survey of Fractional Calculus Neural Network-based (FC NN-based) computer vision techniques for denoising, enhancement, object detection, segmentation, restoration, and NN compression. The survey compiles existing FFC NN-based approaches, elucidates underlying concepts, and identifies open questions and research directions. By leveraging FC's properties, FC NN-based approaches offer a novel way to improve the robustness and efficiency of computer vision systems.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

Neural Fractional Differential Equations (Neural FDE) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represented by a fractional derivative, with a neural network component, forming an initial value problem. During the learning process, both the order of the derivative and the parameters of the neural network must be optimised. In this work, we investigate the non-uniqueness of the optimal order of the derivative and its interaction with the neural network component. Based on our findings, we perform a numerical analysis to examine how different initialisations and values of the order of the derivative (in the optimisation process) impact its final optimal value. Results show that the neural network on the right-hand side of the Neural FDE struggles to adjust its parameters to fit the FDE to the data dynamics for any given order of the fractional derivative. Consequently, Neural FDEs do not require a unique α value, instead, they can use a wide range of α values to fit data. This flexibility is beneficial when fitting to given data is required, and the underlying physics is not known.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

The evolution in semiconducting devices has introduced flexible control on a system but it has also penetrated harmonics in the grid, which results in extra electrical stress and load. Limiting the presence of harmonics in the grid and low power factor maintained by consumers has become of utmost priority to the power system analyst. Hence, the need for Active Filter emerges. Here, a real-time simulation, in dSPACE- Targetlink, of shunt harmonics active filter is propounded. The possible basic control strategy used in the simulation is ”Instantaneous Power Theory”. Control logic of two features of Active Filter viz., Global Harmonics Elimination, and Reactive Power Compensation are produced in the paper. The results obtained in ”Software In Loop Mode” of dSPACE are discussed and verified in detail. The richness of the code generated by the dSPACE- Target link can be reasoned by observing the results which are well aligned with the industrial standards regarding the harmonics.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

Deep learning-based handwriting personality prediction uses neural networks (CNNs) to consider and predict personality characters from handwritten text to improve applications such as adaptive technology and automated data access. This method requires high computational resources and widely classified data, and its accuracy may suffer from signature variation and overfitting. This study introduces a novel optimizeddeep learning for Hand Written Personality Prediction. First the input data is collected from givendataset and an enhanced Gaussian filter is used in pre-processing to improve image quality by reducing noise and increasing contrast.After pre-processing, features are extracted by PCA-based normalized GIST, which standardizes the features to improve image representation.These extracted features are generated using an adaptive horse herd optimization algorithm to select the most important features. Based on selected features Improved Generative Adversarial Networks with artificial hummingbird optimization (IGAN_AHb) enables fast and efficient convergence of GANs. This reduce the mode collapse and ensures training with consistently fine-tuned parameters.The selected features are considered by characters such as openness, conscientiousness, extroversion, agreeableness and neuroticism, and finally classified using the IGAN_AHb classifier. In the result section, the proposed model is compared with various models with the matrix precision, recall, F1-score. The proposed model attained the value of 97.3% of precision and a recall rate of 96%, respectively. By comparing with other models, the proposed model attained highest values.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections, out of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behaviour of our proposed test is examined through extensive Monte Carlo experiments under various data generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labour wage of 36 countries agricultural markets.

This work describes and compares the backpropagation algorithm with the Extended Kalman filter, a second-order training method which can be applied to the problem of learning neural network parameters and is known to converge in only a few iterations. The algorithms are compared with respect to their effectiveness and speed of convergence using simulated data for both, a regression and a classification task.

The inaccurate estimates of linear prediction coefficient (LPC) and noise variance introduce bias in Kalman filter (KF) gain and degrades speech enhancement performance. The existing methods proposed a tuning of the biased Kalman gain particularly in stationary noise condition. This paper introduces a tuning of the KF gain for speech enhancement in real-life noise conditions. First, we estimate noise from each noisy speech frame using a speech presence probability (SPP) method to compute the noise variance. Then construct a whitening filter (with its coefficients computed from the estimated noise) and employed to the noisy speech, yielding a pre-whitened speech, from where the speech LPC parameters are computed. Then construct KF with the estimated parameters, where the robustness metric offsets the bias in Kalman gain during speech absence to that of the sensitivity metric during speech presence to achieve better noise reduction. Where the noise variance and the speech model parameters are adopted as a speech activity detector. The reduced-biased Kalman gain enables the KF to minimize the noise effect significantly, yielding the enhanced speech. Objective and subjective scores on NOIZEUS corpus demonstrates that the enhanced speech produced by the proposed method exhibits higher quality and intelligibility than some benchmark methods.

Exact sequential state estimation of orbiting objects in space can be found by predicting the state using Fokker Planck Kolmogorov Equation (FPKE) and measurement correction using Bayes’ conditional/posterior Probability Density Function (PDF). Posterior PDF can be expressed as Gaussian density expanded in terms of Hermite polynomials named as Gram Charlier Series (GCS). This research is an extension of an earlier work on second order linearized solution to nonlinear Bayesian filtering using Taylor series and third order GCS expansion of posterior PDF. In this new extension, Bayes’ posterior PDF is approximated by a mixture of GCS functions for which the parameters are propagated using linear propagation theory. The update of weights of different components of GCS mixture model uses the FPKE error as feedback to adapt for the amplitude of different GCS components while solving a quadratic programming problem earlier used for Gaussian Mixture Model (GMM) PDF. Proposed filtering method is applied on tracking of space debris. The simulation results for the filter shows performance is moderately better than single GCS filter, Extended Kalman Filter (EKF) and Gaussian Sum Filter (GSF) under space debris’ highly uncertain initial conditions and sparse measurement availability.

This paper presents an alternative process to fabricate flexible bandpass filters by using embroidered yarn conductor on electronic-textile. The novelty of the proposed miniaturized filter is its complete integration on the outfit, with benefits in terms of compressibility, stretch ability and high geometrical accuracy, opening the way to develop textile filters in sport and medicine wearable applications. The proposed design consists of a fully embroidered microstrip topology with a length equal to quarter wavelength (λ/4) to develop a bandpass filter frequency response. A drastic reduction in size of the filter was achieved by taking advantage of a simplified architecture based on meandered-line stepped impedance resonator. The e-textile microstrip filter has been designed, simulated, fabricated and measured, with experimental validation at a 7.58 GHz frequency. The insertion loss obtained by simulation of the filter is substantially small. The return loss is greater than 20 dB for bands. To explore the relations between physical parameters and filter performance characteristics, theoretical equivalent circuit model of the filter constituent components were studied. The effect of bending of the e-textile filter is also studied. The results show that by changing the radius of bending up to 40 mm, the resonance frequency is shifted up 4.25 MHz/mm.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

A new low-pass filter (LPF) circuit with independent adjustment of various, incl. digitally controlled, pole frequency resistors, pole quality factor and transmission coefficient. The proposed low-pass filter is based on the use of the properties of a multi-differential operational amplifier that performs the functions of a signal adder. The peculiarity of the filter is that it has three inputs, with respect to which different transmission coefficients are implemented, incl. inverting (-1) and non-inverting (+1). To check these properties of a low-pass filter in the Micro-Cap environment, computer simulation of a specific circuit was performed on a multi-differential operational amplifier AD 8130. Mathematical expressions are given for the main parameters of the proposed low-pass filter, which allow parametric synthesis of elements of a specific circuit under given restrictions on the used element base.

Determining the vibration environment is crucial to analyzing a design of any mechanical system, especially such dynamic systems as sounding rockets. Accuracy of measurement using accelerometers could be improved by application of mechanical vibration filtering and amplifying devices. This work presents a theoretical description of a tunable filter and amplifier. Principle of work is provided as well as results from application of the device on a sounding rocket are provided. It is shown that implementation of such devices allowed for enhancing the accuracy of acceleration measurements. Conclusions on future implementations are also provided.

Aiming for the problems emerging in the PWM drive system with long cables, accurate modeling of power cables is the premise to predict and analyze the relevant phenomenon, and a proper filter design is the key solution to these problems. This paper proposes high-frequency cable models to represent the frequency-dependent characteristics, especially for the high-frequency resistance of the cable that is an easily overlooked factor but determines the damping of overvoltage. The proposed models can be used for accurately representing the cable parameters in a wide frequency range, and correctly simulating the differential mode (DM) overvoltage and common mode (CM) current, including the peak value, oscillation frequency and damping of the transient waveform. In addition, improved filter networks are proposed to suppress the DM voltage and CM current, with the merit of low losses, small volume and an excellent ability of suppressing overvoltage. The proposed cable models and the filter design have been validated in a 750W PWM drive system with 200m power cables.

We have presented a controllable and human-readable polynomial neural network (CR-PNN) that is the first human-readable neural network. One can imagine its influence on system identification. Subsequently, we developed a relation spectrum in a medical application, which is likely to stand alongside the Fourier spectrum. However, the system analysis methodology is incomplete in contrast to signal processing methodology. Here, we presented the system filters for the first time. In this paper, we used the simulation system to verify the availability of the system analysis methodology. The system analysis methodology showed great properties in system identification and filter. The contribution of this paper is the system analysis methodology: transform method (CR-PNN), relation spectrum, and system filter design.

The purpose of this paper is to provide a structural review of the progress made on detection and localization of leaks in pipelines by using approaches based on the Kalman filter. This is, to the best of our knowledge, the first review on the t opic. In particular, it is the first to try to draw the attention of the leak detection community to the important contributions that use the Kalman filter as the core of a computational pipeline monitoring system. Without being exhaustive, we try to gather the results from different research groups and present them in a unified fashion. For this reason, we propose a classification of the current approaches based on the Kalman filter. For each of the existing approaches within this classification, the basic concepts, fundamental results, and relations with the other approaches are discussed in detail. The review starts from a short summary of basic concepts about state observers. Then, a brief history of the use of the Kalman filter for diagnosing leaks is described by mentioning the most outstanding approaches. At last, we briefly discuss some emerging research problems, such as the leak detection in pipelines transporting heavy oils, and we discuss the main challenges and some open problems.

Loose Tangle is a concept in graph theory that has a dual relationship with branch-width which is well-known graph width parameter. Ultrafilter, a fundamental notion in mathematics, is similarly known to have a dual relationship with branch-width when extended to a connectivity system (X, f). In this compact paper, we revisit and contemplate the interplay between Loose Tangle and Filter through the lens of a submodular partition function.

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

High Efficiency Video Coding (HEVC) uses an 8-point filter and a 7-point filter, which are based on the discrete cosine transform (DCT), for the 1/2-pixel and 1/4-pixel interpolations, respectively. In this paper, discrete sine transform (DST)-based interpolation filters (IF) are proposed. The first proposed DST-based IFs (DST-IFs) use 8-point and 7-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. The final proposed DST-IFs use 12-point and 11-point filters for the 1/2-pixel and 1/4-pixel interpolations, respectively. These DST-IF methods are proposed to improve the motion-compensated prediction in HEVC. The 8-point and 7-point DST-IF methods showed average BD-rate reductions of 0.7% and 0.3% in the random access (RA) and low delay B (LDB) configurations, respectively. The 12-point and 11-point DST-IF methods showed average BD-rate reductions of 1.4% and 1.2% in the RA and LDB configurations for the Luma component, respectively.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

Text-based CAPTCHA remains the most widely adopted security scheme, which is the first barrier to securing websites. Deep learning methods, especially Convolutional Neural Networks (CNNs) are the mainstream approach for text-CAPTCHA recognition, which are widely used in CAPTCHA vulnerability assessment and data collection. However, verification code recognizers are mostly deployed on the CPU platform as part of a web crawler and security assessment, they are required to have both low complexity and high recognition accuracy. Due to the specifically designed anti-attack mechanisms like noise, interference, geometric deformation, twisting, rotation, and character adhesion in text CAPTCHAs, some characters are difficult to efficiently identify with high accuracy in these complex CAPTCHA images. This paper proposed a recognition model named Adaptive-CAPTCHA with a CRNN module and trainable and configurable filtering networks, which effectively handle the interference and learn the correlation between characters in CAPTCHAs to enhance recognition accuracy. Experimental results on two datasets of different complexity show that compared with the baseline model Deep-CAPTCHA, the number of parameters of our proposed model is reduced by about 70% and the recognition accuracy is improved by more than 10 percentage points in the two datasets. In addition, the proposed model has a faster training convergence speed.

The task of determining the distance from one object to another is one of the important tasks solved in robotics systems. Conventional algorithms rely on an iterative process of predicting distance estimates, which results in an increased computational burden. Algorithms used in robotic systems should require minimal time costs, as well as be resistant to the presence of noise. To solve these problems, the paper proposes an algorithm for Kalman combination filtering with a Goldschmidt divisor and a median filter. Software simulation showed an increase in the accuracy of predicting the estimate of the developed algorithm in comparison with the traditional filtering algorithm, as well as an increase in the speed of the algorithm. The results obtained can be effectively applied in various computer vision systems.

Interleaved power factor correction (PFC) is widely used circuit topology due to good efficiency and power density for single-switch boost PFC. As the differential mode (DM) electromagnetic interference (EMI) noise magnitude depends upon the input current ripple, this research details a comprehensive study of DM EMI filter design for interleaved boost PFC with the aim of minimizing the component size. It is also demonstrated that the different numbers of interleaved stages and switching frequency influence the filter attenuation requirement and, thus, the EMI filter size. First, an analytical model is derived on the basis of the Norton equivalent circuit model for the differential mode noises of interleaved boost PFC within the frequency range of 9-500 kHz. The derived model can help identify the optimal phase shifting among the interleaved boost converters in order to minimize the considered differential mode noises at the filter design frequency. So, a novel phase-shift method is developed to get a minimized attenuation required by a filter in Band B. Further, a volume optimization of the required DM filter was introduced based on the calculated filter attenuation and volumetric component parameters. Based on the obtained results, unconventional and conventional phase shifts have demonstrated a good performance in decreasing the EMI filter volume in Band B and Band A, respectively. A 2-kW interleaved PFC case study is presented to verify the theoretical analyses and the impact of phase-shifting on EMI filter size.

During the COVID-19 pandemic face masks grew in importance as their use by the general population was recommended by health officials in order to minimize the risk of infection and prevent further spread of the virus. To ensure health protection of medical personal and other system relevant staff, it is of considerable interest to quickly test if a certain lot of filtering facepiece masks meets the requirements or if the permeability changes under different conditions. As certified penetrometers are rather expensive and were difficult to obtain during the COVID-19 pandemic, we describe two quite simple and cheap methods to quickly test the filter permeability based on an electronic cigarette. The first method uses a precision scale, the second method uses a light scattering detector to measure the filter penetration. To make sure these two methods yield reliable results, both were tested with freshly cut filter samples covering the range of approx. 7% to 60% permeability and compared to the results of a certified penetrometer. The comparison of the two methods with the certified penetrometer showed a good correlation and therefore allow a quick and rather reliable estimation of the permeability. Several examples about the use of faulty masks and the resulting health risks show that simple, fast, cheap and broadly available methods for filter characterization might be useful in these days.

The Bayes filters, such as Kalman and particle filters, have been used in sensor fusion to integrate two sources of information and obtain the best estimate of the unknowns. Efficient integration of multiple sensors requires deep knowledge of their error sources and it is not trivial for complicated sensors, such as Inertial Measurement Unit (IMU). Therefore, IMU error modelling and efficient integration of IMU and Global Navigation Satellite System (GNSS) observations has remained a challenge. In this paper, we develop deep Kalman filter to model and remove IMU errors and consequently, improve the accuracy of IMU positioning. In other words, we add modelling step to the prediction and update steps of Kalman filter and the IMU error model is learned during integration. Therefore, our deep Kalman filter outperforms Kalman filter and reaches higher accuracy.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

We propose a spectral filter based on Plastic Optical Fiber with micro-holes as a low-cost, robust, and highly reproducible spectral filter. The spectral filter is explored for two configurations: fiber extended in a straight line, and a fiber optic loop mirror scheme configuration. The transmission traces indicate a spectral blue shift of peak transmission, at 587 nm, 567 nm, 556 nm, and 536 nm for 0, 1, 2, and 3 holes in the fiber, respectively. The filter exhibits a bandpass period of approximately 120 nm. Additionally, we conducted a comparison of the transmission with holes separated by distances of 1 cm and 500 μm. The results demonstrate that the distance between holes does not alter the spectral transmission of the filter. In the case of the fiber loop mirror configuration, we observed that the bandpass can be adjusted, suggesting the presence of multimode interference. Exploring variations in the refractive index within the holes by filling them with glucose solutions at various concentrations, we determined that the filtering band and spectral shape remains unaltered, ensuring a stable and robust operation of our spectral filter.

Silicon Photomultipliers find applications across various fields. One potential Silicon Photomultiplier application domain is neutrino telescopes, where they may enhance the angular resolution. However, the elevated dark count rate associated with Silicon Photomultipliers represents a significant challenge to their widespread utilization. To address this issue, it is proposed to use Silicon Photomultipliers and Photomultiplier Tubes together. The Photomultiplier Tubes signals would serve as a trigger to mitigate the dark count rate, thereby preventing undue saturation of the available bandwidth. This paper presents an investigation into a fast and resource-efficient method for filtering Silicon Photomultiplier dark count rate. A low-resource and fast coincident filter has been developed, which removes the Silicon Photomultiplier dark count rate by using as trigger the Photomultiplier Tube input signals. The architecture of the coincidence filter, together with the first results obtained, which validate the effectiveness of this method are presented.

The vast rise in the number of Internet-connected devices necessitates a more accessible spectrum. As a result, Cognitive Radio was already proposed as a solution to the problem of restricted spectrum resources by utilizing available spectrum which is assigned to primary users. This method allows the secondary user to utilize the spectrum whenever the primary user is not using it, and it does so without intruding with the primary user. Whenever the secondary user detects the spectrum, it faced some issues, such as complexity in sensing leading to a lack of noise value, and the primary user is hidden to all secondary users. In order to tackle these challenges, an adaptive threshold matched filter detector and a cooperative matched filter detector are utilized in this paper to detect the spectrum. The probability of detection (Pd), probability of miss detection (Pm), and probability of false alarm (Pf) are the metrics used to assess sensing accuracy. To simulate suggested detectors, the MATLAB R2020a software was utilized. In comparison to earlier studies, the simulation conclusions reveal that the detection process starts with lower SNR values.

The on-site wastewater treatment system (OWTS) with a sand trench is an economical option for residents in rural areas or the countryside where a centralised sewer system is inaccessible. 2A sand achieves improved filtration, microbial activity and consistent long term performance when compared to gravel or scoria based trench systems. However, it is expensive and only readily available in a few areas across New Zealand. Additionally, it has a reputation for premature blockage when overloaded or compacted. The aim of this study is not only to critically evaluate the performance of Crushed Glass (CG) with respect to 2A sand, but also to investigate different loading rates for CG when treating primary treated effluent from a septic tank. A test rig was designed and constructed to simulate the real environment of the sand column in a discharge control trench. The treatment efficiency of three filters was recorded and compared in this study. Overall, the CG loaded at 25mm/day (CG₂₅) and 50mm/day (CG₅₀) provided an average of 13% and 6% more Total Nitrogen (TN) reduction than the sand filter, respectively. The removal rates for the TN were up to 69.5%. The CG₅₀ filter performed similarly at 50mm/day as the 2A sand filter in terms of Total Suspended Solids (TSS) and Biochemical Oxygen Demand (BOD)₅ removal of more than 94%. The CG₂₅ removal rates for TSS and BOD₅ at the start of the trial (likely due to residual liquid contamination from the bottles when crushed) improved over the sampling period and ultimately achieved similar results of 92% and 91.3% to the filters loaded at 50mm/day. Lifecycle cost analyses and carbon balances were completed for the two media. It highlighted that the current price of CG is only half of 2A sand, yet it produces significantly less CO₂ emissions than 2A sand. A 3-bedroom dwelling could save up to $500 and reduce 200kg of CO₂ released to the environment annually when 2A sand is substituted for CG. Based on the findings of this paper, it is likely that the reduced installation cost, lessened environmental impact and theoretical availability will lead to CG systems becoming more common in New Zealand and abroad.

The consequences of a fall on an elderly person can be diminished if the accident is attended by medical personnel within the first hour. Independent elderly people use to stay alone for long periods of time, being in more risk if they suffer a fall. The literature offers several approaches for detecting falls with embedded devices or smartphones using a triaxial accelerometer. Most of these approaches were not tested with the objective population, or are not feasible to be implemented in real-life conditions. In this work we propose a Kalman-filter-based fall detection methodology that includes a periodicity detector to reduce the false positive rate. Moreover, this methodology requires a sampling rate of only 25 Hz, it does not require large computations or memory, and it is robust among devices. We tested our approach with the SisFall dataset. Then, we validated it with a new round of simulated activities with young adults and an elderly person achieving 99.4 % of accuracy. Finally, we gave the devices to three elderly persons during two days for full-day validations. They continued with their normal life and the devices behaved as expected.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

Filter Media (FM) sourced from recycled organic and mineral material offers a low cost and effective means of treating urban stormwater. Using recycled materials rather than from an increasingly scarce source of virgin materials (typically sandy loam soil) can ensure a sustainable long-term economy and environment. This paper presents results from the laboratory analysis and mathematical modeling to highlight the performance of recycled organic and mineral material in removing nutrients and metals from stormwater. Analysis included physical and chemical characterisation such as particle size distribution, saturated hydraulic conductivity (Ksat), bulk density, effective cation exchange capacity, and pollutant removal performance. Design mixes (DM), comprising a combination of organic and mineral materials, were characterised and used to develop/derive modelling design within the Model for Urban Stormwater Improvement Conceptualisation (MUSIC v6) [1]. Comparison is made to the Adoption Guidelines for Stormwater Biofiltration Systems - Summary Report [2] which were based on the Facility for Advancing Water Biofiltration (FAWB) guidelines to assist in the development of biofiltration systems, including the planning, design, construction and operation of those systems. An observed outcome from over two decades of biofiltration guideline development has been the exclusion of alternative biofilter materials due to claims of excessive leaching. Results from this study indicate that high nutrient and metal removal rates can be achieved over a range of hydraulic conductivities using design mixes of recycled organic and mineral materials that have a demonstrated equivalence to existing guideline specifications.

In this work, an algorithm was developed to measure the respiration rate for an embedded device that can be used by a field robot for relief operation. With this algorithm, the rate measurement was calculated based on direct influences of respiratory-induced intensity variation (RIIV) on blood flow in cardiovascular pathways. For that, a photoplethysmogram (PPG) sensor was used to determine changes in heartbeat frequencies. The PPG sensor readings were filtered using an Information Filter and a Fast Fourier transform (FFT) to determine the state of RIIV. With a relatively light initialization, the information filter can estimate unknown variables based on a series of measurements containing noise and other inaccuraties. Therefore, this filter is suitable for application on an embedded device. For faster calculation time in the implementation, the FFT analysis was calculated only for a major peak in the frequency domain. Test and measurement of respiration rate was conducted based on the device algorithm and spirometer. Heartbeat measurement was also evaluated by comparing the heartbeat data of the PPG sensor and the medical tool kit. Based on the test, the implemented algorithm can measure respiration rate with about 80% accuracy compared with the spirometer.

Making sustainable business models, especially in manufacturing, is a key approach for organizations to adopt in order to create more sustainable processes. New technologies are needed to implement new policies that can minimize the economic, environmental, and social consequences of industrial activity. Sustainable maintenance is decisive to guarantee the availability, reliability, and safety of assets, surpassing traditional maintenance policies and embracing the principles of the circular economy. The main objective of Maintenance 4.0 is to increase the lifespan and availability of the equipment by preventing unplanned downtime, reducing planned shutdowns, and improving safety. This research focuses on the integration of advanced Industry 4.0 tools with conventional monitoring and control techniques in process industries. The article suggests that while complex neural networks might provide good predictions, simpler solutions can generalize well and have lower prediction errors because they can capture the underlying relationships between variables in a specific asset better. The combination of maintenance function, Industry 4.0 tools, and advanced statistical solutions to obtain sustainable processes can facilitate organizational change and aid decision-making in equipment management. These solutions seek to reduce interruptions and expenses through the unnecessary utilization of labor and spare parts. All these considerations improve communication and data processing, resulting in improved maintenance of a hydrogen compressor in the petrochemical industry.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its extensive use in optics, engineering, and signal processing. In the present work, we aimed to expand the fractional Hilbert transform to a space of generalized functions known as Boehmians. We introduce a new fractional convolution operator for the fractional Hilbert transform to prove a convolution theorem similar to the classical Hilbert transform and also to extend the fractional Hilbert transform to Boehmians. We also construct a suitable Boehmian space on which the fractional Hilbert transform exists. Further, we investigate convergence of the fractional Hilbert transform for the class of Boehmians and discuss the continuity of the extended fractional Hilbert transform.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Arsenic is naturally present in many geological formations around the world and is a major source of groundwater contamination. Bolivia is not exempt from this problem. Physical-chemical studies of water quality in deep and shallow wells have determined the presence of arsenic in some areas of the Bolivian Altiplano, valleys, and plains. In the Lake Poopó basin, water from shallow wells (up to 30 m) has arsenic concentrations that exceed the Bolivian drinking water standard and the WHO recommendation of 10 μg-As/l by up to 25 times. In peri-urban areas of Cochabamba, the arsenic content in groundwater is up to 113 μg-As/l. chronic exposure to arsenic is associated with neurological and dermatological problems and carcinogenic effects. To date, no measures have been taken to mitigate the arsenic problem for the rural population, who often rely on arsenic-contaminated water as their only source of drinking water. This contamination represents a serious threat to the health and economic well-being of the inhabitants and ecosystem in these areas. In this work, for arsenic removal, iron and iron oxide nanoparticles obtained from recycling metal chips by top-down and bottom-up technology have been used for arsenic adsorption in an experimental filter combined with other artisanal filtering materials in the form of layers. The results have shown that water contaminated with arsenic after passing through the filter reduces the concentration of total arsenic filtered from 83, 52 ppb to less than 5 ppb, less than the Bolivian standard 512 of 10 ppb for drinking water.

The paper deals with the Model Predictive Control (MPC) algorithm as applied to the sensorless control of a Permanent Magnet Synchronous Motor (PMSM). The proposed estimation strategy, based on the unscented Kalman filter (UKF), uses only the measurement of the motor current for the online estimation of speed, rotor position and load torque. Information about the system state feeds the MPC. Results verify the effectiveness and applicability of the proposed sensorless control technique. An implementation in low speed direct drive astronomy telescope mount systems is investigated.