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 |
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 |
URI: | http://hdl.handle.net/10773/16181 |
DOI: | 10.1016/j.cnsns.2016.09.006 |
ISSN: | 1007-5704 |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
preprint_RV.pdf | Main article | 361.91 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.