In this paper, we consider the strong convergence of the time-space fractional diffusion equation driven by fractional Gaussion noise with Hurst index $H\in(\frac{1}{2},1)$. A sharp regularity estimate of the mild solution and the numerical scheme constructed by finite element method for integral fractional Laplacian and backward Euler convolution quadrature for Riemann-Liouville time fractional derivative are proposed. With the help of inverse Laplace transform and fractional Ritz projection, we obtain the accurate error estimates in time and space. Finally, our theoretical results are accompanied by numerical experiments.

翻译：在本文中,我们考虑了由分高音驱动的时间-空间分化扩散方程式与赫斯特指数$H_in(\frac{1 ⁇ 2},$1美元)的强烈趋同。对温度溶液的精确定期估计,以及用有限元素方法为里曼-利奥维尔时间分化衍生物的分化分化分化弧和后向变化二次曲线构建的数值方法。在逆拉普尔变异和分位Ritz预测的帮助下,我们获得了时间和空间的准确误差估计。最后,我们理论结果还伴有数字实验。