Regularization for 2-D fractional sideways heat equations

In this article, an inverse problem of Caputo-time-fractional sideways heat equations is considered. The aim is to find the inaccessible boundary data of some heterogeneous materials through interior measurements. Instead of the standard Tikhonov approach, we propose a series of fast filters for reconstructing the missing boundary data. Theoretical error bounds are provided for both boundary and (near-boundary) interior reconstructions. Several numerical examples are included to verify the proven convergence results.