Inverse Source Problem Of The Time Fractional Diffusion Equation

In this thesis, we consider an inverse source problem for a time-fractional diffu-sion equation in a general bounded domain. That is to determine a space-dependent source term in the time-fractional diffusion equation from a noisy final data. We obtain the approximation of the second order derivative of g(x) by using a numerical differ-entiation method. Based on the separation of variables and the properties of fractional derivatives, the approximation of source term can be deduced based on the second order derivative of g(x). Numerical examples show that the proposed method is effective and stable.