  This paper studies the linear stochastic partial differential equation of
fractional orders both in time and space variables $\left(\partial^\beta +
\frac{\nu}{2} (-\Delta)^{\alpha/2} \right) u(t,x)= \lambda u(t,x)
\dot{W}(t,x)$, where $\dot W$ is a general Gaussian noise and $\beta\in (1/2,
2)$, $\alpha\in (0, 2]$. The existence and uniqueness of the solution, the
moment bounds of the solution are obtained by using the fundamental solutions
of the corresponding deterministic counterpart represented by the Fox
H-functions. Along the way, we obtain some new properties of the fundamental
solutions.
