Article
Version 1
Preserved in Portico This version is not peer-reviewed
Conformable Laplace Transform of Fractional Differential Equations
Version 1
: Received: 30 June 2018 / Approved: 3 July 2018 / Online: 3 July 2018 (06:04:53 CEST)
A peer-reviewed article of this Preprint also exists.
Silva, F.S.; Moreira, D.M.; Moret, M.A. Conformable Laplace Transform of Fractional Differential Equations. Axioms 2018, 7, 55. Silva, F.S.; Moreira, D.M.; Moret, M.A. Conformable Laplace Transform of Fractional Differential Equations. Axioms 2018, 7, 55.
Abstract
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.
Keywords
fractional differential equations; conformable derivative; Bernoulli equation; exact solution
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (2)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
Commenter:
The commenter has declared there is no conflict of interests.
This is misleading people.
See
NO NONLOCALITY. NO FRACTIONAL DERIVATIVE.
Vasily E. Tarasov,
What is a fractional derivative?
Ortigueira and Machado
Commenter: Fernando S. Silva
The commenter has declared there is no conflict of interests.
In other words, still seems to us a philosophical and literary question of the type Hamlet: “To be, or not to be, that is the question”!