Exact Controllability for a Class of Fractional Semilinear System of Order 1 < q < 2 with Instantaneous and Noninstantaneous Impulses

Abstract

This paper is mainly concerned with the existence of mild solutions and exact controllability for a class of fractional semilinear system of order $q\in \left(1,2\right)$ with instantaneous and noninstantaneous impulses. First, combining the Kuratowski measure of noncompactness and the Mönch fixed point theorem, we investigated the existence result for the considered system. It is remarkable that our assumptions for impulses and the nonlinear term are weaker than the Lipschitz conditions. Next, on this basis, the exact controllability for the considered system is determined. In the end, an example is provided to support the main findings.