Results on the existence and time optimal control results for Hilfer fractional stochastic differential inclusions in Hilbert spaces

This article mainly focuses into the study of time optimal control for stochastic differential inclusions incorporating the Hilfer fractional derivative in Hilbert spaces. The investigation begins by employing a mathematical framework that integrates fractional calculus, semigroup theory, stochastic analysis, multivalued analysis, and Bohnenblust-Karlin's fixed point theorem to establish the existence of mild solutions for the system. Building on this foundation, the time optimal control results are analyzed, providing deeper insights into the behavior of the system under optimal control constraints. To demonstrate the theoretical results, this study concludes with a detailed application, showcasing the applicability and effectiveness of the proposed methods.