Solvability of a Nonlinear Integro-Differential Equations via Fixed Point Theorem

The aim of the current research, is to investigate the existence of solutions to nonlinear integral-differential equations. It is natural that to establish these innovation achievement, we need mathematical analysis tools in the framework of Banach space, specifically measures of non-compactness and effective fixed point theorem of Petryshyn. Also, based on fixed point theory, we introduce a robust approach to provide the existence of solutions to this type nonlinear equation. Eventually, we examine the applicability of our results by several examples of the equations which can be generalized to a wide range of integral equations.