Dynamics of stochastic nonlocal reaction–diffusion equations driven by multiplicative noise.

This paper deals with fractional stochastic nonlocal partial differential equations driven by multiplicative noise. We first prove the existence and uniqueness of solution to this kind of equations with white noise by applying the Galerkin method. Then, the existence and uniqueness of tempered pullback random attractor for the equation are ensured in an appropriate Hilbert space. When the fractional nonlocal partial differential equations are driven by colored noise, which indeed are approximations of the previous ones, we show the convergence of solutions of Wong–Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as δ → 0. [ABSTRACT FROM AUTHOR]