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Title: Caputo derivatives of fractional variable order: numerical approximations
Author: Tavares, Dina
Almeida, Ricardo
Torres, Delfim F. M.
Keywords: Fractional calculus
Fractional variable order
Fractional differential equations
Approximation methods
Issue Date: Jun-2016
Publisher: Elsevier
Abstract: We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is obtained in terms of standard (integerorder) derivatives only. Estimations for the error of the approximations are also provided. We then compare the numerical approximation of some test function with its exact fractional derivative. We end with an exemplification of how the presented methods can be used to solve partial fractional differential equations of variable order.
Peer review: yes
DOI: 10.1016/j.cnsns.2015.10.027
ISSN: 1007-5704
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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