On a discrete composition of the fractional integral and Caputo derivative

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.Comment: This is an accepted version of the manuscript published in Communications in Nonlinear Science and Numerical Simulations. The changes with the previous versions included some language corrections, additional numerical simulations, and new reference