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 A Caputo fractional derivative of a function with respect to another function
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/16181

title: A Caputo fractional derivative of a function with respect to another function
authors: 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.
URI: http://hdl.handle.net/10773/16181
ISSN: 1007-5704
publisher version/DOI: http://dx.doi.org/10.1016/j.cnsns.2016.09.006
source: Communications in Nonlinear Science and Numerical Simulation
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