an inverse problem for homogeneous time-fractional diffusion problem on the sphere

In this paper, we consider an inverse problem for the time-fractional diffusion equation on the sphere where the final data on the sphere are given. the problem is ill-posed in the sense of hadamard. hence, the regularization method has to be used for the stable approximate solution. then the well-posedness of the proposed regularizing problem and convergence property of the regularizing solution to the exact one is proved. error estimates for this method are provided together with a selection rule for the regularization parameter.