Dynamics of non-autonomous fractional stochastic Ginzburg-Landau equations with multiplicative noise

Abstract

This paper is concerned with the asymptotic behavior of solutions for non-autonomous stochastic fractional complex Ginzburg-Landau equations driven by multiplicative noise with \begin{document}$ \alpha\in(0, 1) $\end{document} . We first apply the Galerkin method and compactness argument to prove the existence and uniqueness of weak solutions, which is slightly different from the deterministic fractional case with \begin{document}$ \alpha\in(\frac{1}{2}, 1) $\end{document} and the real fractional case with \begin{document}$ \alpha\in(0, 1) $\end{document} . Consequently, we establish the existence and uniqueness of tempered pullback random attractors for the equations in a bounded domain. At last, we obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero.