DSpace
 
  Repositório Institucional da Universidade de Aveiro > CIDMA - Centro de Investigação e Desenvolvimento em Matemática e Aplicações > CIDMA - Artigos >
 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
appears in collectionsCIDMA - Artigos

files in this item

file description sizeformat
preprint_RV.pdfMain article361.91 kBAdobe PDFview/open
Restrict Access. You can Request a copy!
statistics

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

 

Valid XHTML 1.0! RCAAP OpenAIRE DeGóis
ria-repositorio@ua.pt - Copyright ©   Universidade de Aveiro - RIA Statistics - Powered by MIT's DSpace software, Version 1.6.2