Existence and controllability of fractional semilinear mixed Volterra-Fredholm integro differential equation

Abstract

In this paper, the existence of mild solution and controllability of fractional semilinear mixed Volterra–Fredholm integro differential equations of order 1<γ<2 with nonlocal conditions are investigated. First we discuss the existence of mild solution and then controllability of the proposed system by using the concept of Banach fixed point theorem and semigroup theory. For the authenticity and applicability of the presented theory some examples are also provided.