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 sum...

Full description

Saved in:
Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2022-05, Vol.108, p.106234, Article 106234
Main Author: Płociniczak, Łukasz
Format: Article
Language:English
Subjects:
Asymptotic methods
Caputo derivative
Composition
Derivatives
Discrete element method
Euler–Maclaurin formula
Fractional calculus
Fractional integral
Fractions
Integrals
Nonlinear equations
Numerical analysis
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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. •The discrete version of the composition mimics the continuous case.•The remainder involves the fractional integral and the derivative of the function.•The remainder with a step h decays to zero at a rate hmin(alpha,1−alpha).
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2021.106234