Application of simulation function and measure of noncompactness for solvability of nonlinear functional integral equations and introduction to an iteration algorithm to find solution

Abstract

The aim of this article is to investigate the existence of solution for the nonlinear functional integral equations with the help of measure of noncompactness, simulation function and generalized Darbo fixed point theorem. Also we provided example for the applicability of obtained results to the theory of integral equations. Also we introduce an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to find solution of the above problem with high accuracy. Finally we have a discussion about convergence and upper bound of error.