Solving generalized nonlinear functional integral equations with applications to epidemic models

Abstract

In this article, we investigate the existence and uniqueness of solutions to a generalized nonlinear functional integral equation (G‐NLFIE) associated with certain epidemic models of infectious diseases, defined within the Banach space . Our existence results include several specific cases of nonlinear functional integral equations that commonly occur in nonlinear sciences. We then introduce an iterative algorithm that combines Adomian's decomposition method (ADM) with the modified homotopy perturbation method (mHPM) to approximate solutions to the G‐NLFIE. The paper addresses the convergence properties and error analysis of this method. Finally, we present numerical examples to demonstrate the effectiveness and efficiency of our proposed approach.