Approximate controllability results for second-order non-local neutral impulsive differential inclusions with damping

Abstract

This paper is mainly concerned with the approximate controllability of damped second-order neutral impulsive differential inclusions with non-local conditions in Banach spaces. We study our primary outcomes by using the theoretical concepts about cosine and sine functions of operators, Bohnenblust and Karlin's fixed point theorem. Using principles and ideas from the theory of the cosine family of operators and the fixed-point approach, we verify the existence of mild solutions for the given system. A new set of sufficient conditions is formulated and proved for the approximate controllability of second-order differential inclusions under the assumption that the associated linear part of the system is approximately controllable. Finally, an application is presented to illustrate our theoretical results.