An Inverse Initial Value Problem For A Time-fractional Difussion Equation

In this thesis, we consider an inverse initial value problem for a time-fractional diffusion equation. That is to determine the initial data from a noisy final data. Since the inverse problem is ill-posed, then we propose a regularization method. Construct a minimization functional in Hilbert scale space and take its mini-mization solution as the regularization solution to deal with the inverse problem. Furthermore we obtain two kinds of convergence rates by using an priori regular-ization parameter choice rule and an a posteriori regularization parameter choice rule. Numerical examples in one-dimensional and two-dimensional cases are pro-vided to show the effectiveness and stability of the proposed methods.