Hilfer fractional neutral stochastic partial differential equations with delay driven by Rosenblatt process

Abstract

This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt process. We discuss the sufficient conditions for approximate controllability and null controllability for Hilfer fractional neutral stochastic partial differential equations driven by Rosenblatt process. Finally, we provide two examples to verify the obtained results.

Keywords:

• Hilfer fractional neutral stochastic integro-differential systems
• approximate controllability
• null controllability
• Rosenblatt process

Mathematics Subject Classifications:

• 93B05
• 34A08
• 60G51

Acknowledgements

The author would like to thank the referees and the editor for their important comments and suggestions, which have significantly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Hamdy M. Ahmed

Hamdy M. Ahmed is Professor of engineering mathematics, affiliated to Department of Physics and Engineering Mathematics, Higher institute of engineering, El Shorouk academy, El-Shorouk city, Cairo, Egypt. His recent research interests include fractional stochastic differential equations, controllability of fractional differential equations and exact solution of nonlinear partial differential equations.