Existence and uniqueness of solutions of nonlinear mixed integrodifferential equations with nonlocal condition in Banach Spaces

Abstract

In this article, we study the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition in Banach spaces. Furthermore, we study continuous dependence of mild solutions. Our analysis is based on semigroup theory and Banach fixed point theorem.

Keywords

• Existence and uniqueness
• mild and strong solutions
• mixed Volterra-Fredholm
• integrodifferential equation
• Banach fixed point theorem
• nonlocal condition