Controllability of neutral stochastic functional integro-differential equations driven by fractional Brownian motion

ABSTRACT

This article focuses on controllability results of neutral stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators developed by Grimmer [Resolvent operators for integral equations in Banach spaces, Trans. Amer. Math. Soc., 273(1982):333–349] combined with a fixed point approach for achieving the required result. An example is provided to illustrate the theory.

Keywords:

• Neutral stochastic partial integro-differential equations
• resolvent operators
• fractional Brownian motion

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G18
• 60G22
• 60H20

Acknowledgments

The author would like to thank the referee and the editor for their careful comments and valuable suggestions on this work. No potential conflict of interest was reported by the author.