Optimal control of higher-order Hilfer fractional non-instantaneous impulsive stochastic integro-differential systems

Nowadays, engineers and biochemical industries have benefited greatly from optimal control analysis and its computational methods. Furthermore, the optimal control theory is a powerful instrument in infectious disease modeling and control of vibration in civil engineering structures under random loadings. In this paper, a new solution representation and optimal control of second-order Hilfer fractional stochastic integro-differential systems (HFSIDSs) with non-instantaneous impulsive (NI) are studied. Existence and uniqueness of solutions are proved in the finite-dimensional space by using Schaefer’s type fixed-point theorem with low conservative conditions on nonlinear part. Further, Lagrange problem is considered to establish optimal control results for HFSIDSs with NI. Finally, a pharmacotherapy type Hilfer fractional model is discussed in the example section.