Hilfer fractional neutral stochastic integro‐differential evolution hemivariational inequalities and optimal controls

Abstract

The focus of this study is a control system with a nonlocal state that is driven by a neutral stochastic integro‐differential evolution hemivariational inequality known as Hilfer fractional (HF). In order to demonstrate effective requirements for the existence of mild solutions to the relevant control system, we first make use of the features of the extended Clarke subdifferential and a fixed point theorem for multivalued functions. We next prove that there are optimal state‐control sets that are induced by HF neutral stochastic integro‐differential evolution hemivariational inequalities with a nonlocal condition by using limited Lagrange optimal structures. The distinctiveness of the control system's solutions is not taken into consideration while developing optimal control outcomes. At last, an example is employed to go over the major findings.