  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.
