Existence and Uniqueness of Mild Solution for Mixed type of Integro-Differential Equation

Abstract

In this paper, we study the existence and uniqueness of a mild solution of a nonlinear mixed Volterra – Fredholm integro-differential equation with nonlocal condition in Banach space. Furthermore, we study continuouce dependence of mild solution. Our analysis is based on semigroup theory and Banach fixed point theorem.

Keywords

• mild solution
• integro-differential equation
• volterra – fredholm