On a discrete composition of the fractional integral and Caputo derivative

07/22/2021

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by   Łukasz Płociniczak, et al.

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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.