Tow-parameter quasi-boundary value method for a backward abstract time-degenerate fractional parabolic problem

Abstract In this article, for a time-degenerate fractional parabolic equation, we study an inverse problem for restoration of the initial condition from the information of the final temperature profile. We show that the considered problem is ill-posed in the sense of Hadamard, i.e., small errors in the measurement data may lead to indefinitely large errors in the solutions. This ill-posed problem is regularized using a modified quasi-boundary value method, and some convergence estimates for the regularized solution are obtained using a priori and posteriori parameter choice rules. Finally, several numerical experiments are presented to demonstrate the accuracy and efficiency of the regularization method.