On numerical approximation of the Riesz-Caputo operator with the fixed/short memory length

被引：7

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：

JOURNAL OF KING SAUD UNIVERSITY SCIENCE | 2021年 / 33卷 / 01期

关键词：

Fractional derivatives; Numerical schemes; Caputo operator; Riesz-Caputo operator; Fixed memory length; FRACTIONAL MODEL;

D O I：

10.1016/j.jksus.2020.10.017

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, the Riesz-Caputo operator is studied. This type of fractional operator is a combination of the left and right Caputo derivatives. The series representation of the analyzed fractional operators with fixed memory length is presented. In the main part of the paper, three modified methods of numerical integration are applied for the approximation of the left and right Caputo, and Riesz-Caputo derivatives. Numerical schemes based on three types of interpolating functions (constant, linear and quadratic function) are presented. The in-depth numerical analysis of the presented schemes is conducted. Absolute errors and experimental rates of convergence, for the considered methods, are calculated and presented. (C) 2020 The Author(s). Published by Elsevier B.V. on behalf of King Saud University.

引用

页数：8

共 37 条

[1] Generalized wave equation in nonlocal elasticity [J].