Approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory

Abstract

We establish results concerning the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory in Hilbert spaces. By using semigroup theory, stochastic analysis techniques and fixed point approach, we derive a new set of sufficient conditions for the approximate controllability of nonlinear stochastic system under the assumption that the corresponding linear system is approximately controllable. Further, the above results are generalized to cover a class of much more general impulsive neutral stochastic delay partial differential equations driven by L?vy noise in infinite dimensions. Finally, an example is provided to illustrate our results.

Approximate controllability of retarded impulsive stochastic integro-differential equations driven by fractional Brownian motion

“…Thus, all the assumptions of Theorem 3.7 are fulfilled. Consequently, the system (18) is approximately controllable on [0, T].…”

“…Boudaoui and Lakhel [8] investigated the controllability results of impulsive neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. Huan et al [18] established results concerning the approximate controllability for time-dependent impulsive neutral stochastic partial differential equations with memory in Hilbert space. Very recently, Lakhel [27] studied the controllability of an impulsive neutral stochastic integro-differential systems with infinite delay driven by fractional Brownian motion in separable Hilbert space.…”

Controllability of Second-Order Stochastic Differential Equations Driven by Fractional Brownian Motion Diem Dang Huan

“…In [27], Sakthivel et al studied approximate controllability of second-order stochastic differential equations with impulsive effects. Very recently, Huan et al [19] established the approximate controllability of the time-dependent impulsive neutral SDEs with memory by using the Holder's inequality, stochastic analysis and fixed point strategy.…”