  Here, we provide a unified framework for numerical analysis of stochastic
nonlinear fractional diffusion equation driven by fractional Gaussian noise
with Hurst index $H\in(0,1)$. A novel estimate of the second moment of the
stochastic integral with respect to fractional Brownian motion is constructed,
which greatly contributes to the regularity analyses of the solution in time
and space for $H\in(0,1)$. Then we use spectral Galerkin method and backward
Euler convolution quadrature to discretize the fractional Laplacian and
Riemann-Liouville fractional derivative, respectively. The sharp error
estimates of the built numerical scheme are also obtained. Finally, the
extensive numerical experiments verify the theoretical results.
