Abstract: The problem of inverting the left boundary of the time-fractional Schrödinger equation in the unbounded region is studied, which is an ill-posed problem, meaning that the solution discontinuously depends on the measurement data. A quasi-boundary regularization method is used to solve this inverse problem, and its regularized solution is given. The error estimates between the regularization solution and the exact solution are derived under the priori and the posteriori regularization parameter selection rule.

Key words: time-fractional Schrödinger equation, inverting the left boundary, ill-posed problem, quasi-boundary regularization method.