Existence of the Solution Via an Iterative Algorithm for Two-Dimensional Fractional Integral Equations Including an Industrial Application

Abstract

We proposed a result which generalizes the Darbo's fixed-point theorem (DFPT) by using measure of noncompactness (MNC). Then, we use DFPT to investigate the existence of the solution of generalized proportional fractional integral equation (FIE) of two variables. Then we present a suitable example to prove the reliability of the method. Also, we use an iterative algorithm based on the modified homotopy perturbation (MHP) method and the sinc interpolation to estimate the solution of the presented example with sufficient precision, and introduce the application of the obtained solution in industry.