The study of parabolic spectral fractional Laplacian with nonhomogeneous Dirichlet boundary conditions

We use characterizations of spectral fractional Laplacian to tackle the problems of parabolic spectral fractional Laplacian incorporating nonhomogeneous Dirichlet boundary conditions. Compared with applying classical extension method in the study of the lower-order fractional operators with $ s \in (0, 1) $, we used a modified extensions to parabolic spectral fractional Laplacian incorporating boundary conditions, adapted from constructing harmonic extensions of the boundary data to spectral fractional Laplacian.