Fractional Tikhonov Method for an Inverse Time-Fractional Diffusion Problem in 2-Dimensional Space

In this paper, we present a new fractional Tikhonov regularization method for solving an inverse problem for a time-fractional diffusion equation which is highly ill-posed in the two-dimensional setting. Fractional Tikhonov regularization method not only retains the advantage of classical Tikhonov method, but also overcomes the effect of over-smoothing of classical Tikhonov method. We give the selection of regularization parameters of the new method and the corresponding error estimation. Furthermore, numerical results show that the fractional Tikhonov method outperforms the classical one.