In this paper, we study two stochastic problems for time-fractional Rayleigh-Stokes equation including the initial value problem and the terminal value problem. Here, two problems are perturbed by Wiener process, the fractional derivative are taken in the sense of Riemann-Liouville, the source function and the time-spatial noise are nonlinear and satisfy the globally Lipschitz conditions. We attempt to give some existence results and regularity properties for the mild solution of each problem.

中文翻译：

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次扩散随机Rayleigh-Stokes方程的初值和终值问题

在本文中，我们研究了时间分数瑞利-斯托克斯方程的两个随机问题，包括初值问题和终值问题。在此，维纳过程扰动了两个问题，从Riemann-Liouville的意义上取分数导数，源函数和时空噪声是非线性的并且满足全局Lipschitz条件。我们试图给出每个问题的温和解的一些存在性结果和正则性质。