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arXiv · 1609.04775

A Caputo fractional derivative of a function with respect to another function

Ricardo Almeida
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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.

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Ricardo Almeida. 2016-09-12. A Caputo fractional derivative of a function with respect to another function. https://doi.org/10.1016/j.cnsns.2016.09.006

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