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September  2019, 18(5): 2409-2431. doi: 10.3934/cpaa.2019109

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

 1 School of Mathematical Science, Sichuan Normal University, Chengdu, Sichuan 610068, China 2 School of Mathematical Science and V.C. & V.R. Key Lab, Sichuan Normal University, Chengdu, Sichuan 610068, China

* Corresponding author

Received  April 2018 Revised  July 2018 Published  April 2019

This paper is concerned with the asymptotic behavior of solutions for non-autonomous stochastic fractional complex Ginzburg-Landau equations driven by multiplicative noise with $\alpha\in(0, 1)$. 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 $\alpha\in(\frac{1}{2}, 1)$ and the real fractional case with $\alpha\in(0, 1)$. 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.

Citation: Yun Lan, Ji Shu. Dynamics of non-autonomous fractional stochastic Ginzburg-Landau equations with multiplicative noise. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2409-2431. doi: 10.3934/cpaa.2019109
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