Optimal feedback control for Sobolev-type nonlocal Hilfer fractional neutral differential system with history-dependent operators
摘要
This study explores optimal feedback control for Sobolev-type fractional neutral evolution system together with non-local conditions in separable, reflexive Banach spaces. As a special case, we considered history-dependent operators in the nonlinear function. The equations incorporate Hilfer fractional derivatives. We first establish the existence of mild solutions by incorporating a fixed-point technique. Subsequently, leveraging the Cesari property and the Filippove theorem, we prove the existence of admissible pairs. We then demonstrate the existence of optimal control pairs for the associated Lagrange control problem. In the end, a concrete example illustrates the applicability and efficacy of the presented theory.