Random Attractors for Fractional Stochastic Hindmarsh-Rose Equations with Memristors

In this paper, we devote to the study of dynamics of fractional stochastic Hindmarsh-Rose equations with memristors and multiplicative noises. We first apply the Galerkin method to prove the existence and uniqueness of the global solutions for the system under consideration. Then, based on some uniform estimates for the solutions we establish the existence and uniqueness of tempered pullback random attractors for the equations in an appropriate Hilbert space. Additionally, the upper semicontinuity of random attractors is also studied as the noise intensity approaches zero.