Controllability and stability of fractional stochastic functional systems driven by Rosenblatt process
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In this paper, we investigate the controllability and exponential stability results for a class of nonlinear neutral stochastic functional differential control systems in the presence of infinite delay driven by Rosenblatt process in real separable Hilbert spaces. Firstly, by using stochastic analysis approach, fractional calculus theory and a fixed point technique, we prove the controllability result for the mild solutions of the nonlinear control systems with the condition that the associated linear system is controllable. Secondly, we discuss the exponential stability of mild solutions of the nonlinear neutral stochastic differential systems driven by Rosenblatt process. Finally, an example is presented to illustrate the obtained theory.
KeywordsFractional stochastic functional systems Controllability Exponential stability Infinite delay Rosenblatt process
Mathematics Subject Classification34K37 34K30 35R11 47N20
This research is supported by the Distinguished Young Scholars Foundation of Anhui Province (1608085J06), the National Natural Science Foundation of China (11271020) and Top talent project of university discipline (specialty) (gxbjZD03).
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