In this talk, we give an introduction to the fractional anomalous diffusion models and related inverse problems. Several kinds of simultaneous inversion problems in the fractional diffusion equations are discussed, including the inverse problem of determining the diffusion coefficient and the fractional order in the TFDE, and the inverse problem of determining the diffusion coefficient and source term in the SFADE and the multi-term TFDE respectively, and the inverse problem of determining the fractional orders and the initial distribution in the TSFDE.
Furthermore, the homotopy regularization algorithm is applied for solving the simultaneous inversion problems, and numerical inversions using noisy data are presented. Several concluding remarks are given for summary of this talk. Joint work with Xianzheng Jia, Chunlong Sun, Guangsheng Chi and M. Yamamoto.