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

• Published in: Journal of engineering mathematics Vol. 146; no. 1
• Main Authors: Sathiyaraj, T., Balasubramaniam, P., Chen, Hao, Ong, Seng Huat
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Control equipment; Control theory; Disease control; Fixed points (mathematics); Infectious diseases; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Optimal control; Theoretical and Applied Mechanics; Hilfer fractional derivative (HFD); Inclusive health; Non-instantaneous impulsive; Optimal control; 26A33; Stochastic differential equations (SDEs); 49N25; 39A50
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-024-10358-y

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.