Computing Hadamard type operators of variable fractional order

被引：19

作者：

Almeida, Ricardo ^{[1
]}

Torres, Delfim F. M. ^{[1
]}

机构：

[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat CIDMA, P-3810193 Aveiro, Portugal

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 257卷

关键词：

Fractional calculus; Variable fractional order; Numerical methods; Fractional differential equations; Fractional calculus of variations; INTEGRATION; DERIVATIVES; DYNAMICS;

D O I：

10.1016/j.amc.2014.12.071

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：74 / 88

页数：15

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