Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift

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