In this talk, I will discuss a Sobolev space theory for the stochastic partial differential equation (SPDE) driven by Wiener processes as well as the SPDE driven by space-time white noise. For the time non-local operator, we consider the Caputo fractional derivative of order $\alpha\in(0,1)$. For the spatial non-local operator, we deal with the infinitesimal generator of the $d$-dimensional subordinate Brownian motion. We prove the uniqueness and existence results in Sobolev spaces and obtain the maximal regularity results of solutions.