  This paper is concerned with the inverse random source problem for a
stochastic time fractional diffusion equation, where the source is assumed to
be driven by a Gaussian random field. The direct problem is shown to be
well-posed by examining the well-posedness and regularity of the solution for
the equivalent stochastic two-point boundary value problem in the frequency
domain. For the inverse problem, the Fourier modulus of the diffusion
coefficient of the random source is proved to be uniquely determined by the
variance of the Fourier transform of the boundary data. As a phase retrieval
for the inverse problem, the PhaseLift method with random masks is applied to
recover the diffusion coefficient from its Fourier modulus. Numerical
experiments are reported to demonstrate the effectiveness of the proposed
method.
