An existence result with numerical solution of nonlinear fractional integral equations

Abstract

By utilizing the technique of Petryshyn's fixed point theorem in Banach algebra, we examine the existence of solutions for fractional integral equations, which include as special cases of many fractional integral equations that arise in various branches of mathematical analysis and their applications. Also, the numerical iterative method is employed successfully to find the solutions to fractional integral equations. Lastly, we recall some different cases and examples to verify the applicability of our study.