On the approximate controllability for neutral fractional stochastic differential hemivariational inequalities with history-dependent operator

This research introduces a novel approach to analyzing neutral fractional stochastic differential system where past behavior influences future outcomes. We leverage fractional derivatives, a powerful mathematical tool that better captures real-world dynamics, along with hemivariational inequalities to account for non-linear relationships within the system. Additionally, a history-dependent operator allows the system's past to influence its current and future behavior. Our focus is twofold: first, we prove the existence of solutions for this intricate system by employing the fixed point theorem, fractional calculus, properties of generalized Clarke's subdifferential and stochastic theory; second, we explore its controllability-the ability to drive it from one state to another within a specific time frame. Finally, we provide an example to bridge the gap between theory and application. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.