On the boundedness analysis of solutions for new class of nonlinear Fredholm integro-differential equations

Abstract

In this work, we present a new class of nonlinear Fredholm integro-differential equations involving two source term functions. Under some hypotheses we prove the existence and uniqueness of solutions for these equations using the Banach fixed point theorem. In addition, we find that this class of equations imposes the boundedness of the derivative of unknown solution as a specific condition among the previous hypotheses, which cannot be found for studying of most integral equation. Besides, we use the numerical Nystr\"{o}m method to approximate the solutions of the proposed equations. Finally, we give some different examples in order to illustrate and support our study.