Reconstruction of the time-dependent source term in a stochastic fractional diffusion equation

Abstract

In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the solution $u$ in integral sense, then prove some theoretical results as uniqueness and stability. After that, we establish a numerical algorithm to solve the unknowns, where the mollification method is used.