A Caputo fractional derivative of a function with respect to another function
Abstract
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem, Fermat's Theorem, etc, are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.
Cite
@article{arxiv.1609.04775,
title = {A Caputo fractional derivative of a function with respect to another function},
author = {Ricardo Almeida},
journal= {arXiv preprint arXiv:1609.04775},
year = {2016}
}
Comments
This is a preprint of a paper whose final and definite form will be published in the journal Communications in Nonlinear Science and Numerical Simulation