Abstract: In this talk, I will present a recent joint-work with Dr. Le Chen, where we study a class of stochastic partial differential equations with fractional differential operators subject to some time-independent multiplicative Gaussian noise. We derive sharp conditions, under which a unique global \(L^p(\Omega)\)-solution exits for all \(p \ge 2\). In this case, we derive exact moment asymptotics following the same strategy in a recent work by Balan et al [1]. In the case when there exists only a local solution, we determine the precise deterministic time, \(T_2\), before which a unique \(L^2(\Omega)\)-solution exits, but after which the series corresponding to the \(L^2(\Omega)\) moment of the solution blows up. By properly choosing the parameters, results in this paper interpolate the known results for both stochastic heat and wave equations.