Existence of solutions for some classes of integro-differential equations on ${C^1}(\mathbb{R}_{+})$ by applying a measure of noncompactness

Abstract

This paper introduces sufficient conditions for the existence of solutions in some classes of integro-differential equations. Due to Darbo's fixed point theorem with an appropriate measure of noncompactness, we prove the existence of solution in each class of equations. Finally, some significant examples are solved using the artificial small parameter method.Mathematics Subject Classification (2010). 47H10, 45J05, 47H08.