ABSTRACT This paper deals with the asymptotic behaviour of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by multiplicative noise with . We first present some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Then we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equations in . At last, we prove the finiteness of fractal dimension of random attractors.

中文翻译：

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具有乘性噪声的非自治分数随机 Ginzburg-Landau 方程的随机吸引子的分形维数

摘要 本文讨论了由乘法噪声驱动的非自治随机分数阶 Ginzburg-Landau 方程解的渐近行为。我们首先提出了一些限制非自治随机动力系统的随机不变集的分形维数的条件。然后我们导出解的统一估计，并建立 中方程的缓和回拉随机吸引子的存在性和唯一性。最后，我们证明了随机吸引子的分形维数的有限性。