Optimal Feedback Control Results for Hilfer Fractional Neutral Dynamical Systems with History-Dependent Operators

This paper presents a systematic approach for analyzing optimal feedback control systems governed by Hilfer fractional neutral evolution equations with history-dependent operators in separable reflexive Banach spaces. We initially investigate the existence of mild solutions for the system using the Darbo-Sadovskii fixed point theorem. Subsequently, feasible pairs were established by applying the Filippov theorem and the Cesari property. Furthermore, we demonstrate the existence of optimal control pairs for the associated Lagrange control problem. Finally, an illustration is provided to highlight the effectiveness of our findings.