In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2} \in(0,\frac{1}{2}]$. We first provide the regularity of the solution. Then we employ the Wong-Zakai approximation to regularize the rough noise and discuss the convergence of the approximation. Next, the finite element and backward Euler convolution quadrature methods are used to discretize spatial and temporal operators for the obtained regularized equation, and the detailed error analyses are developed. Finally, some numerical examples are presented to confirm the theory.
翻译：在这项工作中,我们有兴趣建立完全分离的随机分解扩散方程式,该方程式由分块的布朗平板驱动,在时间和空间上是分数的,具有赫斯特参数$H ⁇ 1},H ⁇ 2}(in) (0)\frac{1 ⁇ 2}$。我们首先提供解决方案的规律性。然后,我们用黄 ⁇ 近似法来规范粗噪音,并讨论近似值的趋同。接下来,使用有限的元素和后向脉冲二次曲线方法将获得的正统方程式的空间和时间操作器分解,并进行详细的错误分析。最后,我们提出了一些数字例子来证实理论。
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