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Title: Computing Hadamard type operators of variable fractional order
Author: Almeida, R.
Torres, D. F. M.
Keywords: Fractional calculus
Fractional calculus of variations
Fractional differential equations
Numerical methods
Variable fractional order
Differential equations
Differentiation (calculus)
Torque control
Fractional derivatives
Fractional derivatives and integrals
Fractional operators
Fractional order
Numerical procedures
Variational problems
Issue Date: 2015
Publisher: Elsevier
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.
Peer review: yes
DOI: 10.1016/j.amc.2014.12.071
ISSN: 0096-3003
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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