What is the fractional Laplacian? A comparative review with new results

The fractional Laplacian in Rd, which we write as (−Δ)α/2 with α∈(0,2), has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 404; p. 109009
Main Authors:	Lischke, Anna, Pang, Guofei, Gulian, Mamikon, Song, Fangying, Glusa, Christian, Zheng, Xiaoning, Mao, Zhiping, Cai, Wei, Meerschaert, Mark M., Ainsworth, Mark, Karniadakis, George Em
Format:	Journal Article
Language:	English
Published:	Cambridge Elsevier Inc 01.03.2020 Elsevier Science Ltd Elsevier
Subjects:	Anomalous diffusion Approximation Boundary conditions Boundary value problems Collocation methods Computational physics Domains First principles Fractional Laplacian MATHEMATICS AND COMPUTING Nonlocal model Numerical analysis Numerical methods Operators (mathematics) Poisson equation Radial basis function Regularity Spectra Stable Lévy motion Stable Lévy motion Nonlocal model Fractional Laplacian Regularity Anomalous diffusion
ISSN:	0021-9991, 1090-2716
Online Access:	Get full text
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