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.

如今，工程师和生化工业已经从最优控制分析及其计算方法中受益匪浅。此外，最优控制理论是随机载荷下土木工程结构的传染病建模和振动控制的强大工具。本文研究了非瞬时脉冲（NI）二阶 Hilfer 分数随机积分微分系统（HFSIDS）的新解表示和最优控制。利用非线性部分低保守条件的Schaefer型不动点定理，在有限维空间中证明了解的存在唯一性。此外，考虑拉格朗日问题来建立具有 NI 的 HFSIDS 的最优控制结果。最后，示例部分讨论了药物治疗类型 Hilfer 分数模型。