Fractional Laplacian in Bounded Domains

Abstract

The fractional Laplacian operator, $-(-△{)}^{\frac{\alpha }{2}}$, 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

References in corpus (2)

• Width distribution of contact lines on a disordered substrate
• Some Insights in Superdiffusive Transport

Cited by in corpus (2)

• The Spectrum of the Fractional Laplacian and First Passage Time Statistics
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