  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.
