Solving Abel integral equations of first kind via fractional calculus
Classical Analysis and ODEs
2015-03-13 v1 Numerical Analysis
Abstract
We give a new method for numerically solving Abel integral equations of first kind. An estimation for the error is obtained. The method is based on approximations of fractional integrals and Caputo derivatives. Using trapezoidal rule and Computer Algebra System Maple, the exact and approximation values of three Abel integral equations are found, illustrating the effectiveness of the proposed approach.
Keywords
Cite
@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}
}
Comments
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