Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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.

Journal reference: Axioms 2018, 7, 55
DOI: 10.3390/axioms7030055

## 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

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

Comment 1
Commenter: Manuel Ortigueira
The commenter has declared there is no conflict of interests.
Comment: It's difficult to understand why an operator that is a product of a power by an integer order derivative is called "fractional".

See
NO NONLOCALITY. NO FRACTIONAL DERIVATIVE.
Vasily E. Tarasov,
What is a fractional derivative?
+ Respond to this comment
Response 1 to Comment 1
Commenter: Fernando S. Silva
The commenter has declared there is no conflict of interests.
Comment: Indeed, we have not discussed the possibility given in these two beautiful articles. We should put a remark on this topic. However, the conformable fractional derivative be or not be a fractional derivative seems still unresolved and so it is a topic that still deserves to be studied.

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”!

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