On a final value problem for the time-fractional diffusion equation with inhomogeneous source.

In this paper, we consider an inverse problem for the time-fractional diffusion equation with inhomogeneous source to determine an initial data from the observation data provided at a later time. In general, this problem is ill-posed, therefore we construct a regularizing solution using the quasi-boundary value method. We also proposed both parameter choice rule methods, thea-prioriand thea-posteriorimethods, to estimate the convergence rate of the regularized methods. In addition, the proposed regularized methods have been verified by numerical experiments, and a comparison of the convergence rate between thea-prioriand thea-posteriorichoice rule methods is also given. [ABSTRACT FROM AUTHOR]