Time-Optimal Control of Hilfer Fractional Stochastic Hemivariational Inequalities Analysis

This manuscript investigates the time optimal control results for a class of fractional stochastic hemivariational inequalities governed by the Hilfer derivative. The analysis begins by establishing existence results for the underlying system using tools from fractional calculus, stochastic analysis, semigroup theory, and multivalued analysis, together with fixed-point theorems for multivalued mappings. Building on these foundational results, time optimal control conditions are derived under a set of suitable and verifiable assumptions. To illustrate the applicability and effectiveness of the proposed framework, a detailed example is provided, demonstrating how the theoretical results can be employed to achieve optimal performance in systems exhibiting both memory effects and stochastic behavior.