New Numerical Approach for Solving Abel's Integral Equations

Ayşe Anapalı Şenel, Yalçın Öztürk, Mustafa Gülsu
2021 Foundations of Computing and Decision Sciences  
In this article, we present an efficient method for solving Abel's integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then substituting their matrix forms into the equation. The main character behind this technique's approach is that it reduces such problems to solving a system of algebraic
more » ... quations, thus greatly simplifying the problem. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. Figures and tables are demonstrated to solutions impress. Also, all numerical examples are solved with the aid of Maple.
doi:10.2478/fcds-2021-0017 fatcat:ycv5a2g5dnat3mfci2qjlqw4jq