Exact and trajectory controllability of second-order evolution systems with impulses and deviated arguments

In this paper, we consider a control system represented by a second-order evolution impulsive problems with delay and deviated arguments in a Banach space X. We used the strongly continuous cosine family of linear operators and fixed-point method to study the exact controllability. Also, we study the trajectory controllability of the considered control problem. Finally, an example is provided to illustrate the application of the obtained abstract results.