Abstract In this paper, we prove the existence and regularity of a tempered pullback attractor for a non-autonomous stochastic fractional equation involving an abstract non-local operator defined as where is the kernel of which satisfies the general fractional-type condition of order and is a ball in centered at x with radius ε. The asymptotical compactness of solutions in is demonstrated by the spectral decomposition and truncation technique, where is a Hilbert space with and As a special example, we obtain the existence and regularity of tempered pullback attractor of stochastic fractional reaction-diffusion equation.

中文翻译：

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乘法白噪声驱动的非自治非局部分数方程的调和随机吸引子

摘要 在本文中，我们证明了一个非自治随机分数方程的调和回拉吸引子的存在性和规律性，该方程涉及一个抽象的非局部算子，定义为 其中 核满足一般分数型阶条件，并且是一个以 x 为中心、半径为 ε 的球。解的渐近紧性由谱分解和截断技术证明，其中 是一个带有 和 的希尔伯特空间 作为一个特例，我们得到了随机分数反应扩散方程的回火吸引子的存在性和规律性。