关于分数阶积分与 Caputo 导数的离散复合
数值分析
2023-09-07 v3 数值分析
摘要
我们证明了分数阶积分与 Caputo 导数复合的一个离散类比。当用所谓的 L1 格式离散化 Caputo 导数时，该结果在分数阶偏微分方程的数值分析中具有重要意义。证明基于利用 Euler-Maclaurin 求和公式对离散和进行渐近估计。
引用
@article{arxiv.2107.10489,
title = {On a discrete composition of the fractional integral and Caputo derivative},
author = {Łukasz Płociniczak},
journal= {arXiv preprint arXiv:2107.10489},
year = {2023}
}
备注
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 references