Regularization for a fractional sideways heat equation

We consider a sideways problem for a fractional heat equation which is highly ill-posed. This study gives a new dynamic method for choosing a regularization parameter. By using the spectral methods, some convergence rates on the temperature and heat flow are given. For illustration, several numerical examples are constructed to show the feasibility and efficiency of the proposed methods. Comparing with the traditional stationary methods for choosing regularization parameter, the proposal methods are more accurate and effective.