On a discrete composition of the fractional integral and Caputo derivative

被引：0
|
作者：
Plociniczak, Lukasz [1 ]
机构：
[1] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2022年 / 108卷
关键词：
Fractional integral; Caputo derivative; Euler-Maclaurin formula;
D O I：
10.1016/j.cnsns.2021.106234
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a discrete analogue for the composition of the fractional integral and Caputo derivative. This result is relevant in numerical analysis of fractional PDEs when one discretizes the Caputo derivative with the so-called L1 scheme. The proof is based on asymptotic evaluation of the discrete sums with the use of the Euler-Maclaurin summation formula. (C) 2022 Elsevier B.V. All rights reserved.
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