Fractional Landweber Regularization Method for Identifying the Source Term of the Time Fractional Diffusion-Wave Equation

In this paper, the inverse problem of identifying the source term of the time fractional diffusion-wave equation is studied. This problem is ill-posed, i.e., the solution (if it exists) does not depend on the measurable data. Under the priori bound condition, the condition stable result and the optimal error bound are all obtained. The fractional Landweber iterative regularization method is used to solve this inverse problem. Based on the priori regularization parameter selection rule and the posteriori regularization parameter selection rule, the error estimation between the regularization solution and the exact solution is obtained. Moreover, the error estimations are all order optimal. At the end, three numerical examples are given to prove the effectiveness and stability of this regularization method.