On Solution of Nonlinear Integral and Fractional Differential Equations via Discontinuous Nonlinear Contractions

Abstract

The aim of this research work is to demonstrate the survival of exactly one common fixed point for nonlinear contractions without assuming containment of range spaces of an involved pair of mappings, commutativity, and continuity (or any of their weaker forms). It is interesting to note that these findings involve different techniques of proof and comparatively fewerassumptions related to underlying mappings to find the existence of common fixed points of certain mappings. In this way, such investigations are generalizations and improvements over the several prominent recent results of the existing literature. For the application part, we solve the system of nonlinear integral equations of Fredholm and Volterra type and fractional differential equation of Caputo type to validate our results. Moreover, we validate the main conclusion with the help of an example.