Approximate controllability analysis of impulsive neutral functional hemivariational inequalities

This article mainly focuses on the existence and approximate controllability of impulsive neutral functional hemivariational inequalities. The existence of mild solutions and approximate controllability results are formulated and proved by using the semigroup of operators theory, a fixed point theorem of multivalued maps, and properties of generalized Clarke subdifferential. In the end, some examples are provided to illustrate the applicability of the main results. •The existence and approximate controllability of impulsive neutral functional hemivariational inequalities are examined.•Theories of semigroup, hemivariational inequalities and Clark’s subdifferential type are used for discussing the primary outcomes.•We begin by proving the existence of mild solutions of the considered system.•Next, approximate controllability of impulsive neutral functional control system are proved.•Finally, some applications are provided for drawing the theory of the primary outcomes.