Caputo derivatives of fractional variable order: Numerical approximations

被引：145

作者：

Tavares, Dina ^{[1
,2
]}

Almeida, Ricardo ^{[2
]}

Torres, Delfim F. M. ^{[2
]}

机构：

[1] Polytechn Inst Leiria, ESECS, P-2411901 Leiria, Portugal

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

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2016年 / 35卷

关键词：

Fractional calculus; Fractional variable order; Fractional differential equations; Approximation methods; ANOMALOUS DIFFUSION; OPERATORS; EQUATION;

D O I：

10.1016/j.cnsns.2015.10.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：69 / 87

页数：19

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