Optimal control of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps

Abstract

In this work, the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative. First, we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus, successive approximation method and stochastic analysis techniques. Second, the optimal control of the proposed problem is presented by using Balder's theorem. Finally, an example is demonstrated to illustrate the obtained theoretical results.

Keywords:

• Hilfer fractional derivative
• stochastic integrodifferential systems
• Rosenblatt process
• Poisson jumps
• successive approximation
• optimal control

Acknowledgments

The authors would like to thank the helpful comments and suggestions of the Associate Editor and the anonymous reviewers, which have improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

K. Ramkumar

K. Ramkumar received M.Sc. degree from Ramakrishna Mission, Vivekanandha College, Madras University, and Ph.D. from PSG College of Arts and Science, Coimbatore, Bharathiar University, India. Currently working as an assistant professor at PSG College of Arts and Science, Coimbatore. The research interest includes control theory, stochastic differential systems.

K. Ravikumar

K. Ravikumar received M.Sc. degree from Ramakrishna Mission, Vivekanandha College, Madras University, and Ph.D. from PSG College of Arts and Science, Coimbatore, Bharathiar University, India. Currently working as an assistant professor at PSG College of Arts and Science, Coimbatore. The research interest includes control theory, stochastic differential/integro-differential systems.

E. M. Elsayed

E. M. Elsayed received Ph.D. degree in pure Mathematics from Faculty of Science, Mansoura University, Egypt, in 2006. Currently working as a professor of Mathematics, Mathematics Department, Faculty of Science, King Abdulaziz University, Kingdom of Saudi Arabia. The research interest includes Difference Equations including Local stability, Global stability, Semi-cycles, Oscillation, Periodicity; Differential Equations.