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Title: A Caputo fractional derivative of a function with respect to another function
Author: Almeida, Ricardo
Keywords: Fractional calculus
Semigroup law
Numerical methods
Population growth model
Issue Date: Mar-2017
Publisher: Elsevier
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.
Peer review: yes
DOI: 10.1016/j.cnsns.2016.09.006
ISSN: 1007-5704
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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