Fourier regularization for solving sideways problem of a nonlinear time-fractional diffusion equation

This paper studies the sideways problem of a nonlinear time-fractional diffusion equation. This is a severely nonlinear ill-posed problem, and a Fourier regularization method is used to solve the problem. We derive a priori error estimates and a posteriori error estimates of the regularization solution under a priori parameter and a posteriori parameter choice rules, respectively. Numerical results show the stability and effectiveness of the proposed regularization method.