New discussion regarding approximate controllability for Sobolev-type fractional stochastic hemivariational inequalities of order r∈(1,2)

In this paper, we deal with the approximate controllability of Sobolev-type fractional stochastic evolution hemivariational inequalities of order r∈(1,2). Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, and fixed point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution systems. Next, our results cover problems involving nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study. •Approximate controllability of fractional hemivariational inequalities are studied.•Stochastic theory, multimaps, and fixed point approach are used in the main results.•We begin by proving the existence of mild solutions of the considered system.•Next, approximate controllability of fractional stochastic control system are proved.•At last, some examples are provided to define the primary results.