@Article{JCM-43-615,
author = {Ye , XingyangCao , Junying and Xu , Chuanju},
title = {A High Order Scheme for Fractional Differential Equations with the Caputo-Hadamard Derivative},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {43},
number = {3},
pages = {615--640},
abstract = {<p style="text-align: justify;">In this paper, we consider numerical solutions of the fractional diffusion equation with
the $α$ order time fractional derivative defined in the Caputo-Hadamard sense. A high
order time-stepping scheme is constructed, analyzed, and numerically validated. The contribution of the paper is twofold: 1) regularity of the solution to the underlying equation
is investigated, 2) a rigorous stability and convergence analysis for the proposed scheme
is performed, which shows that the proposed scheme is $3 + α$ order accurate. Several
numerical examples are provided to verify the theoretical statement.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2312-m2023-0098},
url = {http://global-sci.org/intro/article_detail/jcm/23552.html}
}