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.

翻译：我们证明了分数阶积分与Caputo导数复合的离散类似物。该结果在使用所谓L1格式离散化Caputo导数的分数阶偏微分方程数值分析中具有相关性。证明基于利用欧拉-麦克劳林求和公式对离散和进行渐近评估。