Computing Hadamard type operators of variable fractional order

Ricardo Almeida and Delfim F.M. Torres

Applied Mathematics and Computation, 2015, vol. 257, issue C, 74-88

Abstract: We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard–Marchaud fractional derivative, is also considered. The objective is to represent these operators as series of terms involving integer-order derivatives only, and then approximate the fractional operators by a finite sum. An upper bound formula for the error is provided. We exemplify our method by applying the proposed numerical procedure to the solution of a fractional differential equation and a fractional variational problem with dependence on the Hadamard–Marchaud fractional derivative.

Keywords: Fractional calculus; Variable fractional order; Numerical methods; Fractional differential equations; Fractional calculus of variations (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:74-88

DOI: 10.1016/j.amc.2014.12.071

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