We examine the asymptotic behavior of the non-autonomous non-local fractional stochastic reaction-diffusion equations on $ \mathbb{R}^{N} $ with the nonlinearity $ f $ satisfying the polynomial growth of arbitrary order $ p-1 $ $ (p\geq2) $. We first establish a Nash-Moser-Alikakos type a priori estimate for the difference of solutions near the initial time. Then, we prove that the solution process is continuous from $ L^{2}(\mathbb{R}^{N}) $ to $ H^{s}(\mathbb{R}^{N}) $ with respect to initial data for $ s\in(0, 1) $. As an application of the higher-order integrability and the continuity, we obtain the pullback $ \mathcal{D} $-random attractors in $ L^{p}(\mathbb{R}^{N}) $ and $ H^{s}(\mathbb{R}^{N}) $, respectively. This is a natural and necessary extension of current existing results to further understand the dynamics of the underlying problem.

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非自治分数阶反应扩散方程的动力学 \begin{document}$ \mathbb{R}^{N} $\end{document} 由乘法噪声驱动

我们研究了 $ \mathbb{R}^{N} $ 上非自治非局部分数随机反应扩散方程的渐近行为，其非线性 $ f $ 满足任意阶数的多项式增长 $ p-1 $ $ (p\geq2) $。我们首先建立 Nash-Moser-Alikakos 类型的对初始时间附近解的差异的先验估计。然后，我们证明求解过程从 $ L^{2}(\mathbb{R}^{N}) $ 到 $ H^{s}(\mathbb{R}^{N}) $ 是连续的到 $ s\in(0, 1) $ 的初始数据。作为高阶可积性和连续性的应用，我们在 $ L^{p}(\mathbb{R}^{N}) $ 和 $ H^ 中获得了回调 $ \mathcal{D} $-随机吸引子{s}(\mathbb{R}^{N}) $，分别。这是对当前现有结果的自然且必要的扩展，以进一步了解潜在问题的动态。