Approximation and application of the Riesz-Caputo fractional derivative of variable order with fixed memory

被引：14

作者：

Blaszczyk, Tomasz ^{[1
]}

Bekus, Krzysztof ^{[1
]}

Szajek, Krzysztof ^{[2
]}

Sumelka, Wojciech ^{[2
]}

机构：

[1] Czestochowa Tech Univ, Dept Math, Al Armii Krajowej 21, PL-42200 Czestochowa, Poland

[2] Poznan Univ Tech, Inst Struct Anal, Piotrowo 5 St, PL-60965 Poznan, Poland

来源：

MECCANICA | 2022年 / 57卷 / 04期

关键词：

Riesz-Caputo derivative; variable order; fractional continua; numerical solution; ANOMALOUS DIFFUSION; NUMERICAL-SOLUTION; NONLOCAL ELASTICITY; CONTINUUM-MECHANICS; HEAT-CONDUCTION; EQUATION; CALCULUS; MODEL; BEAM; STABILITY;

D O I：

10.1007/s11012-021-01364-w

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator is approximated by means of modified basic rules of numerical integration. The three proposed methods are based on polynomial interpolation: piecewise constant, piecewise linear, and piecewise quadratic interpolation. The errors generated by the described methods and the experimental rate of convergence are reported. Finally, an application of the Riesz-Caputo fractional derivative of space-dependent order in continuum mechanics is depicted.

引用

收藏

页码：861 / 870

页数：10

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