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.

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.

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.

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.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

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.

In this paper, we propose to explore a nonlinear fractional mathematical model of HFMD- Hand Foot Mouth Disease with vaccinated compartment. Firstly, we prove the non negativity and boundedness for the fractional order dynamical model. The system’s existence and uniqueness are studied using the formulation of the Caputo derivative operator. The fixed-point approach was used to get results indicating the presence of at least one solution. In numerical simulation, we obtained the approximate solution by using fractional Euler method.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

The fractional telegraph partial differential equation with fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. Laplace method is used to find the exact solution of this equation. Stability inequalities are proved for the exact solution. Difference schemes for the implicit finite method are constructed. The implicit finite method is used to deal with modelling the fractional telegraph differential equation defined by Caputo fractional of Atangana-Baleanu (AB) derivative for different interval. Stability of difference schemes for this problem is proved by the matrix method. Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the proposed method.

In this work, we introduce a new and generalized concept (herein referred to as Caputo fractional delta derivative and Caputo fractional delta dini derivative of order $\alpha\in(0,1)$) for Caputo fractional derivatives on an arbitrary time domain $\mathbb{T}$ which is a closed subset of $\mathbb{R}$. Combining the continuous and discrete time domains, we create a unified framework for stability analysis on time scales. Comparison results and stability criteria for the considered Caputo fractional dynamic equations are presented based on a new definition for Caputo fractional delta derivative of a Lyapunov function, contributing to the broader understanding of fractional calculus on time scales. The work also incorporates an illustrative example to demonstrate the relevance, effectiveness and applicability of the established stability results over that of the integer order.

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.

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.

Fractional differential systems have received much attention in recent decades likely due to its powerful ability in modeling memory processes, which are mostly observed in real world. Fractional models have been widely investigated and applied in many fields such as physics, biochemistry, electrical engineering, continuum and statistical mechanics. It is shown by many researchers that fractional derivatives can provide more accurate models than integer order derivatives do. Obviously, bang-bang property is of a significant importance in optimal control theory. In this paper a Bang-Bang property and time-optimal control problem for time-Fractional Differential System (FDS) is under consideration. First we formulate our problem and we prove the existence theorem. We state and prove the bang-bang theorem. Finally we give the optimality conditions that characterized the optimal control. Some illustrate applications are given to clarify our results.

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.

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 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.

This paper predict and effectively control the temperature distribution of the steady-state and transient states of anisotropic four-layer composite materials online, knowing the density, specific heat, heat conductivity and thickness of the composite materials. Based on the transfer function, a mathematical model was established to study the dynamic characteristics of heat transfer of the composite materials. First of all, the Fourier heat transfer law was used to establish a one-dimensional Fourier heat conduction differential equation for each composite layer, and the Laplace transformation was carried out to obtain the system function. Then the approximate second-order transfer function of the system was obtained by Taylor expansion, and the Laplace inverse transformation was carried out to obtain the transfer function of the whole system in the time domain. Finally, the accuracy of the simplified analytical solutions of the first, second and third order approximate transfer functions was compared with computer simulation. The results showed that the second order approximate transfer functions can describe the dynamic process of heat transfer better than others. The research on the dynamic characteristics of heat transfer in the composite layer and the dynamic model of heat transfer in composite layer proposed in this paper have a reference value for practical engineering application. It can effectively predict the temperature distribution of composite layer material and reduce the cost of experimental measurement of heat transfer performance of materials.

In this manuscript a new approach into analyzing the local stability of equilibrium points of non-linear Caputo fractional planar systems is shown. It is shown that the equilibrium points of such systems can be a stable focus or unstable focus. In addition, it is proposed that previous results regarding the stability of equilibrium points have been incorrect, the results here attempt to correct such results. Lastly, it is proposed that a Caputo fractional planar system cannot undergo a Hopf bifurcation, contrary to previous results prior. Though, it is shown that such systems can undergo a Hopf bifurcation (topologically).

This paper presents a demonstration of a linearly-polarized transmit-arrays antenna with high-efficiency and wideband operating in X-band. The topology of the unit cell consists of two identical patch antennas loaded by C-loop slot and interconnected by a metalized via through a ground plane sandwiched between two identical substrates [18]. A waveguide measurement system WGMS has been used for single cell characterization (reflection/transmission coefficients). Good results have been demonstrated in terms of matching performances; the reflection coefficient S11 is under 10-dB in the 9.4-10.4 GHz band (i.e. 10.1% around 9.9 GHz) and with only 0.35 dB-insertion loss at 10 GHz. The transmit-arrays prototype permitted to achieve 22.4 dBi of directivity and 20.1 dBi of gain. The aperture and radiation efficiencies are about 28.2% and 58.3%, respectively. With a focal ratio (F/D) of 1/2 the spill-over loss is less than 2 dB. Beam-scanning up to ± 35° has been achieved with the same phase quantization (passive) and less than 3 dB of gain losses.

The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to the integer order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

Glycine in its neutral form can exist in the gas phase while its zwitterion form is more stable in water solution.But how many waters are actually necessary to stabilize the zwitterionic structure in the gas phase? Are the intramolecular isotropic spin spin coupling constants sensitive enough to accuse the change in the environment? or the conformer observed? These and related questions have been investigated by a computational study at the level of density functional theory employing the B3LYP functional and the 6-31++G**-J basis set. We found that at least two water molecules explicitly accounted in the super-molecule structure are necessary to stabilize both conformers of glycine within a water polarizable continuum model. At least half of the SSCC’s of both conformers are very stable to changes in the environment and at least four of them differ significantly between Neutral and Zwitterion conformation.

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

This study develops a new definition of fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. Such developed definition encompasses many types of fractional derivatives, such as the Riemann-Liouville and Caputo fractional derivatives for singular kernel type as well as the Caputo-Fabrizio, the Atangana-Baleanu and the generalized Hattaf fractional derivatives for non-singular kernel type. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, newly numerical scheme is developed to approximate the solutions of a class of fractional differential equations (FDEs) involving the mixed fractional derivative. Finally, an application to computational biology is presented.

The main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

The use of salt rock for underground radioactive waste disposal facilities requires a comprehensive analysis of creep-damage process in salt rock. A computer-controlled creep setup is employed to carry out a creep test of salt rock lasted as long as 359 days under a constant uniaxial stress. The AE space-time evolution and energy releasing characteristics during creep test are studied in the meantime. A new creep-damage model is proposed on the basis of fractional derivative by combining the AE statistical regularity. It indicates that the AE data in non-decay creep process of salt rock can be divided into three stages. Furthermore, the parameters of new creep-damage model are determined by Quasi-Newton method. The fitting analysis suggests that the creep-damage model based on fractional derivative in this paper provides a precise description of full creep regions in salt rock.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The result obtained is the approximation of the real value. There are few reports on the approximate error and the applicable condition. In this paper, according to the fractional expansions, we study the factors related to the approximate errors. Our research shows that the approximate errors relate not only to fractional order but also to time $t$ and increase rapidly with time $t$. This method can only be applied within a certain time range and the time range is relevant to fractional order and fractional expansions. Then, many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

Covid-19 is a lung disease caused by a Coronavirus family virus. Due to its extraordinary prevalence and death rates, it has spread quickly to every country in the world. Thus, achieving peaks and outlines and curing different types of relapses is extremely important. Given the worldwide prevalence of Coronavirus and the participation of physicians in all countries, Information has been gathered regarding the properties of the virus, its diverse types, and the means of analyzing it. Numerous approaches have been used to identify this evolving virus. It is generally considered the most accurate and acceptable method of examining the patient's lungs and chest through a CT scan. As part of the feature extraction process, a method known as fractional Fourier transform (FrFT) has been applied as one of the time-frequency domain transformations. The proposed method was applied to a database consisting of 2481 CT images. Following the transformation of all images into equal sizes and the removal of non-lung areas, multiple combination windows are used to reduce the number of features extracted from the images. In this paper, the results obtained for KNN and SVM classification have been obtained with accuracy values of 99.84% and 99.90%, respectively.

This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated "peaks" and "fat" tails is also discussed.

Four discrete models using the exact spectral derivative discretization finite difference (ESDDFD) method are proposed for a chaotic five-dimensional, conformable fractional derivative financial system incorporating ethics and market confidence. Since the system considered was recently studied using the conformable Euler finite difference (CEFD) method and found to be hyperchaotic, and the CEFD method was recently shown to be valid only at fractional index , the source of the hyperchaos is in question. Through numerical experiments, illustration is presented that the hyperchaos previously detected is in part an artifact of the CEFD method as it is absent from the ESDDFD models.

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

The electroencephalogram (EEG) is a record of brain activity. Brain Computer Interface (BCI) technology formed by the EEG signal has become one of the hotspots at present. How to extract the feature signal of EEG is the most basic research of BCI technology. In this paper, A new method of recognizing fatigue, conscious, concentrated state of human brain is proposed by the combination of discrete wavelet transform and the neural network based on EEG signal. First of all, the law signal is preprocessed by the wavelet denoising method because the law EEG signal contains a large number of high frequency noise, which is decomposed into multi-layer high frequency signal and low frequency signal. thus, δ wave, θ wave, α wave, β wave are obtained by the wavelet transform. And then, frequency band energy of the different wave is regards as the feature signal of EEG. In the experiment, the feature signal is classified by radial basic function (RBF) and annealed chaotic competitive learning network (ACCLN). RBF and ACCLN networks are trained with 500 sets of sample data and are tested by 100 sets of samples in different mental states. The experimental results show that the average accuracy of RBF network under three conditions are 88.75%, 88.25%, 88.5%, respectively, and the correct rate of ACCLN network is 97%, 98%, 98%, respectively.

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.

The Stepped Frequency Waveform (SFW) is commonly employed in radar technology to synthesize wideband signals through the aggregation of narrow-band pulses, thereby achieving high-resolution range profiles without the need to increase the radar's instantaneous bandwidth. However, the inherent large time-bandwidth product of SFW introduces substantial ranging errors and energy dispersion, which significantly hinders its efficacy in detecting high-speed objects. This paper introduces a pioneering velocity estimation technique utilizing the fractional Fourier transform (FrFT) to address these limitations. Leveraging the characteristic of the Doppler signal from a moving target, which manifests as a chirp signal with a rate proportional to the target's velocity, the FrFT is utilized for precise velocity estimation. Subsequent to this, velocity compensation is applied using the deduced metrics, followed by the application of the inverse fast Fourier transform (iFFT) to pinpoint the target's exact location. To optimize the computational efficiency of determining the FrFT's optimal order, we propose an iterative algorithm founded on the golden section search method. The effectiveness of the proposed approach is verified by simulation data, and the results demonstrate that the proposed approach can accurately estimate the velocity and the range of the high-speed targets with a relatively low computational complexity.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

The radiative heat transfer in arc plasma models is considered from the point of view of its description in terms of a net emission coefficient, the method of spherical harmonics in its lowest order, and the discrete ordinate method. Net emission coefficients are computed applying approximate and numerical approaches, the multi-band representation of the spectral absorption coefficient with three kinds of its averaging and two datasets. The self-consistent access to the radiative heat transfer is applied to a two-dimensional axisymmetric model of free-burning arc in argon at atmospheric pressure. The results obtained from the models employing the net emission coefficient, the method of spherical harmonics, and the discrete ordinate method are compared.

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana-Baleanu fractional derivatives without singular and local kernel having strong memory. The human blood is considered as base fluid dispersing carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes(MWCNTs )) into it to form blood-CNTs nanofluid. The nanofluids are considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood-SWCNTs by reason of higher thermal conductivity whereas, this trend is opposite in case of velocity profile due densities difference.

The goal of the current study is to analyse several nonlinear two-dimensional time-fractional Rosenau Hymanequations. The two-dimensional fractional Rosenau-Hyman equation has extensive use in engineering and applied sciences. The fractional view analysis of two-dimensional time-fractional Rosenau-Hyman equations is discussed using the homotopy perturbation approach, adomian decomposition method, and Yang transformation. Some examples involving two-dimensional time-fractional Rosenau-Hyman equations are provided in order to better understand the suggested approaches. The solutions appear as infinite series. We offer a comparison between the accurate solutions and those that are generated employing the proposed approaches in order to demonstrate the effectiveness and applicability of the proposed techniques. The results are graphically illustrated using 2D and 3D graphs. It has been noted that the obtained results and the targeted problems real solutions are quite similar. Calculated solutions at various fractional levels describe some of the problems useful dynamics. Other fractional problems that arise in other fields of science and engineering can be solved using a modified version of the current techniques.

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.

Medical image segmentation is a critical step in various healthcare applications, aiding in diagnosis, treatment planning, and disease monitoring. In this study, we investigate the efficacy of a segmentation approach based on the 2D wavelet transform. Leveraging a dataset comprising 10 diverse medical images, we evaluate the performance of our segmentation method using three key metrics: accuracy, precision, and recall. Our findings demonstrate that the proposed approach enhances segmentation accuracy, offering promising results compared to existing methods. By harnessing the multi-resolution feature extraction capabilities of the 2D wavelet transform, our method achieves improved delineation of medical image structures, paving the way for more accurate and efficient healthcare interventions.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

Kim-Kim ([9]) studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace Transformation and investigate some properties and formulas related to them.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

The aim of this study is to analyse problems related to thermal mapping obtained from thermal data acquired from Unmanned Aerial Systems (UAS) equipped with thermal cameras. We focused on an accurate analysis of uncertainties introduced by the PIX4D Mapper software used to obtain the surface temperature maps of thermal images acquired by the UAS. To achieve this aim, we used artificial thermal reference during the surveys, as well as natural hot targets, i.e. thermal anomalies in the Pisciarelli hydrothermal system in Campi Flegrei caldera (CFc). Artificial thermal targets, expressly created and designed for this goal, are a prototype here called “developed thermal target” (DTT) made by the drone Laboratory at Istituto Nazionale di Geofisica e Vulcanologia - Osservatorio Vesuviano (INGV-OV). We show the results obtained by three surveys during which thermal targets were positioned on land at different flight heights of the UAS. Different heights were also necessary to test spatial resolution of the DTT with the used thermal camera as well as possible temperature differences between the raw images acquired by UAS with the thermal mapping obtained from the PIX4D Mapper software. In this work we have estimated the uncertainty that may be introduced by the mosaic procedure and furthermore we find an attenuation of the measured temperatures introduced by the different distances between the thermal anomaly and sensor. These results appear to be of great importance for the subsequent calibration phase of the thermal maps especially in cases where these methodologies are applied for monitoring purposes of volcanic/geothermal areas.

There are rich proper noun derivative semantic relationships in geographic entity vector data. The identification of traditional proper noun derivative semantic relationships usually requires toponym researchers to examine the source of derived toponyms by consulting a large number of toponym documents. This method cannot adapt to the mining of proper noun derivative semantic relationships for large-scale geographical entity. In this regard, this paper proposes a method of identifying the proper noun derivative semantic relationships for geographical entity by combining prompt learning and XGBoost model. This method transforms the extraction problem of proper noun derivative semantic relationships into a binary classification problem by analyzing the characteristics of the derivation relationship of toponyms in the form of toponyms and the spatial and temporal distribution of geography. Firstly, prompt learning and gaussian mixture model are used to extract and cluster the derivation words of toponyms, so as to realize the recognition of derived toponyms collections. Then, enumerate the possible proper noun derivations in the toponym set, and then the XGBoost model is used to identify the semantic relations derived from the proper noun of geographical entities. In the experiment, the recognition method of proper noun derivative semantic relationships based on prompt learning and XGBoost proposed in this paper has achieved good relationship recognition effect in the experiment. This method has certain practical value in the fields of toponym management and toponym translation.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

A time integration scheme based on semi-Lagrangian advection and Laplace transform adjustment has been implemented in a baroclinic primitive equation model. The semi-Lagrangian scheme makes it possible to use large time steps. However, errors arising from the semi-implicit scheme increase with the time step size. In contrast, the errors using the Laplace transform adjustment remain relatively small for typical time steps used with semi-Lagrangian advection. Numerical experiments confirm the superior performance of the Laplace transform scheme relative to the semi-implicit reference model. The algorithmic complexity of the scheme is comparable to the reference model, making it computationally competitive, and indicating its potential for integrating weather and climate prediction models.

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.

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.

Previous control methods developed by our research team cannot satisfy the high-accuracy requirements of unmanned surface vessel (USV) path-tracking during bathymetric mapping because of the excessive overshoot and slow convergence speed. For this reason, this study developed an adaptive fuzzy integral-derivative line-of-sight (AFIDLOS) guidance law for USV path-tracking control. Integral and derivative terms were added to counteract the effect of the sideslip angle, with which the USV could be quickly guided to converge to the planned path for bathymetric mapping. To obtain a high-accuracy of the look-ahead distance, a fuzzy control method was proposed. The proposed method was verified using simulations and outdoor experiments. The results demonstrate that the AFIDLOS guidance law can reduce the overshoot by 79.85%, shorten the settling time by 55.32% in simulation experiments, and reduce the average cross-track error by 10.91%, and can ensure a 30% overlap of neighboring strips of bathymetric LiDAR outdoor mapping when compared with the traditional method.

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.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

In this paper, a multibody calculation methodology has been applied to the vibration analysis of a 4-cylinder, 4-stroke, turbocharged diesel engine, with a simulation driven study of the angular speed variation of a crankshaft under consideration of different modeling assumptions. Moreover, time dependent simulation results, evaluated at the engine supports, are condensed to a vibration index and compared with experimental results, obtaining satisfactory outcomes. The modal analysis also considers the damping aspects and has been conducted using a multibody model created with the software AVL/EXCITE. The influence of crankshaft torsional frequencies on the rotational speed behavior has been evaluated in order to reduce the vibration phenomena.

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.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

The twisted Wang transform distribution family, defined as the composition of parameter shifted inverse CDF function with an original CDF function, is found to be most suitable for matching low shape factor distributions, characterizing hard to fit or to simulate reinsurance portfolio losses for some perils from our previous study. Among them, the best form for matching a hard-to-fit empirical loss distribution for a specific peril, is the Exponential Fractional Extra Power 0 Distribution in (0,1) with CDF:.The simplest yet still a good form of this family is the Transformed Hyperbolic Tangent Distribution with CDF:,which has analytical formulas for the moments. The twisted Wang transform distribution family is compared and confirmed to be superior to all other well-known distribution families through extensive numerical optimization practice, distribution forms guesses, and computer-aided exploration 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.

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

Sentiment analysis to characterize properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy transform to capture stylized facts and mutual connections between time series having different nature. Six years of daily Bitcoin Prices and Google Trends are analyzed in order to establish new perspectives in the management of their dynamics.

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.

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.

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.

(1) Background: The aim of the work was to characterize the climatic evolution and change based on the Multi Criteria Classification through the dynamics of bioclimatic indices in viticulture across Italy and its regional administrative boundaries, focusing on latitudes and elevations. (2) Methods: The impact of climate change on viticulture in Italy was analysed and spatialized with reference to historical data from 1991 to 2021 and to the Future Scenarios up to 2080 assumed by SSP2-4.5 and SSP5-8.5, taking into account 13 GCMs. (3) Results: The bioclimatic indices have all shown a significant trend in the historical period, with an increase in temperature and a decrease in precipitation, reflecting their effects on the entire Italian territory with respect to HI, up to 44°N for CI and up to 46°N for DI, regardless of altitude. The Future Scenarios highlighted a shift towards the warmer classes of the two temperature-based indices (HI and CI) for both SSPs, especially for altitudes up to 900 m a.s.l.. The DI-based classification based on DI remained relatively stable in Italy over time, although DI values will become increasingly negative in the near future. (4) Conclusions: The climate in Italy is warming, especially in the south and in the coastal regions. By 2080, more areas will be “Very Hot” with “Warm Nights.” Drought will also increase and have a negative impact on viticulture. The importance of higher latitudes and altitudes in mitigating the effects of climate change justifies the continuing trend towards the relocation of vineyards as a medium-term solution and as an alternative to targeted cultivation methods that must be adopted in the short-term to safeguard the suitability of an area to quality viticulture.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

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.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

Bitumen aging is the major factor which contributes to the deterioration of the road pavement. Oxidation and volatilization are generally considered as the most important phenomena affecting aging in asphalt paving mixtures. The present study was carried to investigate whether various antioxidants provided by natural resources such as phospholipids, ascorbic acid as well as lignin from rice husk, could be used to reduce age hardening in asphalt binders. A selected bituminous material was modified by adding 2 % w/w of the anti-aging natural additives and subjected to accelerated oxidative aging regimes according to the Rolling Thin Film Oven Test (RTFOT) method. The effects of aging were evaluated based on changes in sol-gel transition temperature of modified bitumens measured through Dynamic Shear Rheology (DSR). Moreover, changes of Electron Paramagnetic Resonance (EPR) spectra were monitored on the bituminous fractions asphaltene and maltene separated by solvent extraction upon oxidative aging. The phospholipids-treated binder exhibited the highest resistance to oxidation and the lowest age-hardening effect compared to the other tested anti-oxidants. The combination of EPR and DSR techniques represents a promising method for elucidating the changes in associated complex properties of bitumen fractions promoted by addition of free radical scavengers borrowed by green resources.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

Hepatitis B surface antigen (HBsAg) is not only the biomarker of hepatitis B virus (HBV) infection and expression activity in hepatocytes, but also contributes to viral specific T cell exhaustion and HBV persistent infection. Therefore, anti-HBV therapies targeting HBsAg to achieve HBsAg loss are key approaches for HBV functional cure. In this study, we found that YZH-106, a rupestonic acid derivative, inhibited HBsAg secretion and viral replication. Further investigation demonstrated that YZH-106 promoted the lysosomal degradation of viral L- and M-HBs proteins. Mechanistic study by Biacore and docking analysis revealed that YZH-106 bound directly to PreS2 domain of L- and M-HBsAg, thereby blocking their entry to the endoplasmic reticulum (ER) and promoting their degradation in cytoplasm. Our work thereby provide basis for design of novel compound therapy to target HBsAg against HBV infection.

Nowadays the preservation and restoration of historical building needs to be faced in accordance with a novel sensibility regarding environment to preserve the future generations. In this context, the scientific community is focusing on novel and sustainable materials and techniques allowing durability and mechanical performances and at the same time compatibility with the existing heritage. Alkali activated materials represent a great challenge to produce new materials starting from the existing ones with reducing consumption, emission of greenhouse gases and environmental impact. This study deals with the valorization of waste materials coming from demolition and construction activities in the manufacture of geocomposites suitable for restoration and conservation of historical heritage. In particular, waste from tuff sawing and brick grinding were used as raw materials, then the geopolymeric samples produced were characterized from physical-chemical and mechanical point of view in order to investigate their performance and evaluate their suitability as materials for historical buildings recovery. Brick waste based geocomposites resulted to be more compact than the tuff-based ones as showed by the higher density values and the lower values of open porosity and water absorption and as further confirmed by the trend of the mechanical performance. Moreover, experimental data showed that physical and mechanical properties of both bricks and tuff waste-based geocomposites, even with different waste content, are compatible with existing building materials and to all the traditional repairing products.

Recently Candida auris has emerged as a multi-resistant fungal pathogen, with a significant clinical impact, and has become a critical issue in WHO fungal priority list, due to its unique ability to persist for long time on human skin and hospital environments. It is therefore fundamental to reinforce hospital surveillance protocols to limit nosocomial outbreaks. The study purpose was the Fourier-Transform Infrared Spectroscopy (FT-IR) application to investigate the phylogenetic relationships between isolated strains within the C. auris outbreak at the university Intensive Care Unit of a Tertiary University hospital in Turin (Italy). In order to calculate a clustering cut-off, intra- and inter-isolates distance values were analysed. Data showed the presence of a major cluster Alfa and a minor cluster Beta with a defined C. auris clustering cut-off. The results were validated by an external C. auris strain and Principal Component and Linear Discriminant Analysis. The application of FT-IR technology had allowed to obtain important information about the phylogenetic relationships between the analysed strains, defining for the first time a “not WGS-based” clustering cut-off with a statistical-mathematical approach. FT-IR could represent a valid alternative to molecular methods for rapid and cost saving typing of C. auris strains with important clinical implications.

Under suitable continuity and uniqueness conditions, solutions of an α order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used is a standard technique and makes heavy use of recent results for differentiation of solutions of Caputo fractional intial value problems with respect to initial conditions and continuous dependence for Caputo fractional boundary value problems.

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

We consider rotational hypersurface in the four dimensional Euclidean space. We calculate the mean curvature and the Gaussian curvature, and some relations of the rotational hypersurface. Moreover, we define the third Laplace-Beltrami operator and apply it to the rotational hypersurface.

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.

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 rhizosphere is a rich source of actinomycetes which can produce several potential biologically-active secondary metabolites. The principal goals for this research are to extract, purify and characterize the bioactive secondary metabolites produced by three different strains of actinomycetes isolated from the rhizosphere of rosemary, black locust and olive. The plant growth-promoting effect (PGPE) of the studied strains of actinomycetes on Ocimum basilicum L. (basil) and disease-control effect on necrotic stem lesions of “black leg” caused by Fusarium tabacinum on basil, were in silico evaluated. The cell-free culture filtrates from the studied actinomycetes isolates were evaluated in vitro for their antimicrobial activity against some common phytopathogens. The secondary metabolites obtained from the cell-free culture filtrates have been chemically characterized using high‐resolution electrospray ionization of liquid-chromatography/mass-spectrometric detection (ESI-(HR)Orbitrap-MS). Results of in silico trial showed that all studied isolates demonstrated PGPE on basil seedlings improving some Eco-physiological characteristics and reduced the disease incidence of F. tabacinum. The extracted metabolites from the studied actinomycetes demonstrated antimicrobial activity in Petri-plates assay. The chemical analysis revealed the presence of totally 20 different components. This research emphasizes how valuable the examined isolates are for producing bioactive compounds, indicating their putative antimicrobial activity and their potential employment as fungal-biocontrol agents. In particular, the obtained results revealed the possibility of green-synthesis of some important secondary metabolites such as N-Acetyl-L-histidinol, Rhizocticin A and Eponemycin from actinomycetes. The bioactive metabolites may be successively used to develop novel bio-formulations for both crop protection and/or PGPE.

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.

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.

In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

A classical origin for the Bohmian quantum potential, as that potential term arises in the quantum mechanical treatment of black holes and Einstein-Rosen (ER) bridges, can be based on 4th-order extensions of Einstein's equations. In Bohm's ontological interpretation, black hole radiation, and the analogous tunneling process of quantum transmission through an ER bridge, are classically allowed if the dynamics are modified to include such a quantum potential. The 4th-order extension of general relativity required to generate the quantum potential is given by adding quadratic curvature terms with coefficients that maintain a fixed ratio, as their magnitudes approach zero. Quantum transmission through the classically non-traversable bridge is replaced by classical transmission through a traversable wormhole. If entangled particles are connected by a Planck-width ER bridge, as conjectured by Maldacena and Susskind, then the classical wormhole transmission effect gives the ontological nonlocal connection between the particles posited in Bohm's interpretation of their entanglement. It is hypothesized that higher-derivative extensions of classical gravity can account for the nonlocal part of the quantum potential generally.

This review is focused on synephrine, the principal phytochemical found in bitter orange and other medicinal plants, and widely used as a dietary supplement for weight loss/body fat reduction. We examine different aspects of synephrine biology, delving into its established and potential molecular targets, as well as its mechanisms of action. We present an overview of the origin, chemical composition, receptors, and pharmacological properties of synephrine, including its anti-inflammatory and anti-cancer activity in various in vitro and animal models. Additionally, we conduct a comparative analysis of the molecular targets and effects of synephrine with those of its metabolite, selective glucocorticoid receptor agonist (SEGRA) Compound A (CpdA), which shares a similar chemical structure with synephrine. SEGRA, including CpdA, have been extensively studied as glucocorticoid receptor activators that have a better benefit/risk profile than glucocorticoids due to the reduced adverse effects. We discuss the potential of synephrine usage as a template for the synthesis of new generation of non-steroidal SEGRA. The review also provides insights into the safe pharmacological profile of synephrine.

This article studies electrostatic fields and potentials in the presence of conductors and point charges under the framework of solving Laplace’s equation with specifi ed boundary conditions. The results demonstrate that many problems posed and solved in elementary electrostatics through various heuristics such as the method of images, can be more rigorously treated under the solution framework of Laplace’s equation.

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

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

We study how abstract representations emerge in a Deep Belief Network (DBN) trained on benchmark datasets. Our analysis targets the principles of learning in the early stages of information processing, starting from the “primordial soup" of the under-sampling regime. As the data is processed by deeper and deeper layers, features are detected and removed, transferring more and more “context-invariant” information to deeper layers. We show that the representation approaches an universal model – the Hierarchical Feature Model (HFM) – determined by the principle of maximal relevance. Relevance quantifies the uncertainty on the model of the data, thus suggesting that “meaning" – i.e. syntactic information – is that part of the data which is not yet captured by a model. Our analysis shows that shallow layers are well described by pairwise Ising models, which provide a representation of the data in terms of generic, low order features. We also show that plasticity increases with depth, in a similar way as it does in the brain. These findings suggest that DBNs are capable of extracting a hierarchy of features from the data which is consistent with the principle of maximal relevance.

In this work we present a novel steganography algorithm, based on Fractal Transform domain, combined with the principles of Cryptography. The proposed method uses a private key, which will indicate which segment of the image will be taken and encoded with the Fractal Transform, to then insert the secret bits in the transformed coefficients, thus generating the stego image.

In this article we derive a closed form expression for the symmetric logarithmic derivative of Fermionic Gaussian states. This provides a direct way of computing the quantum Fisher Information for Fermionic Gaussian states. Applications range from quantum Metrology with thermal states to non-equilibrium steady states with Fermionic many-body systems.

Retinitis Pigmentosa, defined more properly as rod-cone dystrophy, is the paradigm of diffuse inherited retinal dystrophies, one of the rare diseases with the highest prevalence in the worldwide population and one of the main causes of low vision in pediatric and elderly age groups. Advancement and understanding in molecular biology and gene editing technologies raised the interest in putting the basis for new therapeutic strategies in rare diseases. As a consequence, new possibilities for clinicians and patients are arising due to the feasibility of treating such a devastating disorder reducing its complications. The scope of this review is to focus on the pathomolecular mechanisms underlying RP better to understand the prospective for its treatment with innovative approaches.

The control of the three-dimensional (3D) polymer network structure is important for permselective materials when specific biomolecules detection is needed. Here we investigate conditions to obtain a tailored hydrogel network that combine both molecular filtering and molecular capture capabilities for biosensing applications. Along this line short oligonucleotide detection in a displacement assay is set within PEGDA hydrogels synthetized by UV radical photopolymerization. To provide insights on the molecular filter capability, diffusion studies of several probes (sulforhodamine G and dextrans) with different hydrodynamic radii were carried out using NMR technique. Moreover, fluorometric analyses of hybridization of DNA oligonucleotides inside PEGDA-hydrogels shed light on the mechanisms of recognition in 3D, highlighting that mesh size and crowding effect greatly impact of hybridization mechanism onto polymer network. Finally, we found the best probe density and diffusion transport conditions to allow the specific oligonucleotide capture and detection inside PEGDA-hydrogels for oligonucleotide detection and the filtering out of higher molecular weight molecules.

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.