Error of discretization of Caputo fractional derivative in weighted spaces
Numerical Analysis
2026-04-27 v1 Numerical Analysis
Abstract
We establish uniform error bounds of the L1 discretization of the Caputo fractional derivative of the function from the weighted Sobolev space with weight belonging to the Mucknenhoupt class. We present how our framework works for several examples of weight, which belong to the Muckenhoupt class. As and application, we show the convergence of the L1 scheme for the Fractional ODE. Finally, we verify the theoretical results with numerical illustrations.
Keywords
Cite
@article{arxiv.2604.22470,
title = {Error of discretization of Caputo fractional derivative in weighted spaces},
author = {Łukasz Płociniczak and Hubert Woszczek},
journal= {arXiv preprint arXiv:2604.22470},
year = {2026}
}