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 Euler-Maclaurin summation formula.

翻译：我们证明对分数集成和卡普托衍生物的构成是一个离散类比。 当一个将卡普托衍生物与所谓的L1方案分离时,这一结果与分数PDE的数值分析相关。 证据的基础是使用Euler- Maclaurin 配和公式对离散金额进行无症状评估。