A solution to a nonlinear Fredholm integro-differential equation

Abstract

This paper deals with a Fredholm integro-differential equation with nonlinear integral term. By using the Dzhumabaev parametrization method, we reduce the equation to a special Cauchy problem and establish sufficient conditions for the existence of its unique solution.  The solution to the special Cauchy problem is used to construct a new general solution to the Fredholm integro-differential equation. We  investigate some properties of the new general solution and apply it to boundary value problems.