An Inverse Source Problem Of A Time-fractional Diffusion Equation

This paper is devoted to identify a time-dependent source term in a time-fractional diffusion equation from boundary solute concentration measurement. The existence and uniqueness for the direct problem with Neumann boundary condition are provided. We propose a variational method to solve the inverse problem and use the conjugate gradient method to solve the optimization problem. We also prove the uniqueness for the inverse source problem. Numerical examples in one-dimension and two-dimension cases are provided to show the effectiveness of the proposed method.