Caputo derivatives of fractional variable order: numerical approximations

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 (integer-order) 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.

This is a preprint of a paper whose final and definite form is in Communications in Nonlinear Science and Numerical Simulation, ISSN: 1007-5704. Paper submitted 27/May/2015; revised 06/Oct/2015; accepted 30/Oct/2015

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