Qualitative analysis of improved order Hilfer fractional feedback control differential inclusions with Volterra-integral

This work primarily aims to investigate the existence of feedback control for a class of Hilfer fractional integro-differential inclusions of order 1<η<2. Initially, we establish sufficient conditions using fractional calculus, cosine families, multivalued mappings, Volterra integral operators, and the Bohnenblust-Karlin fixed point theorem, which underpins the main existence results. Furthermore, by applying the Cesari property and Filippov's theorem, we derive comprehensive criteria guaranteeing the existence of feasible control pairs for the given problem. These findings are subsequently generalised to optimal feedback control pairs through the Lagrange problem, thereby expanding the scope of feedback control methodologies. Finally, a detailed theoretical example is presented to illustrate the obtained results.