Fractional Laplacian in Bounded Domains
Abstract
Description
The fractional Laplacian operator, $-(-\triangle)^{\fracα{2}}$, appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained.
11 pages, 11 figures
11 pages, 11 figures