通过分数阶微积分求解第一类 Abel 积分方程
经典分析与常微分方程
2015-03-13 v1 数值分析
摘要
我们提出了一种数值求解第一类 Abel 积分方程的新方法，并获得了误差估计。该方法基于分数阶积分和 Caputo 导数的近似。利用梯形法则和计算机代数系统 Maple，求得了三个 Abel 积分方程的精确值和近似值，从而说明了所提方法的有效性。
引用
@article{arxiv.1409.8446,
title = {Solving Abel integral equations of first kind via fractional calculus},
author = {Salman Jahanshahi and Esmail Babolian and Delfim F. M. Torres and Alireza R. Vahidi},
journal= {arXiv preprint arXiv:1409.8446},
year = {2015}
}
备注
This is a preprint of a paper whose final and definite form is in Journal of King Saud University (Science), ISSN 1018-3647. Paper submitted 30/Aug/2014; revised 25/Sept/2014; accepted for publication 29/Sept/2014