A New Approach on the Approximate Controllability Results for Hilfer Fractional Stochastic Hemivariational Inequalities of Order \(1<\mu <2\)

In this paper, we investigate the approximate controllability for Hilfer fractional stochastic hemivariational inequalities of order \(1<\mu <2\) $1<\mu <2$ in Hilbert spaces. Initially, we define the concept of a mild solution for our problem in terms of fractional calculus, cosine families, stochastic analysis, and generalized Clarke subdifferential. Then, the existence and approximate controllability for Hilfer fractional stochastic evolution hemivariational inequalities are formulated and proven under appropriate conditions using fixed point theorems for multivalued maps. Finally, an example is presented to illustrate the theory.