Fractional stochastic evolution hemivariational inequalities and optimal controls

Abstract

This paper investigates the existence of mild solutions for fractional stochastic evolution hemivariational inequalities and optimal controls. An existence theorem concerned with the mild solution for the presented system is proved by means of the fractional calculation, stochastic analysis theory, Bohnenblust-Karlin fixed point theorem and some properties of the Clarke subdifferential. Moreover, an existence result of optimal control pair that governed by a fractional stochastic evolution hemivariational inequality is also obtained. Finally, an example is given for demonstration.