Abstract: The fractional Laplacian operator -(-delta)(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 eigenvalue spectrum are also obtained.
Publication Year: 2007
Publication Date: 2007-08-01
Language: en
Type: article
Indexed In: ['pubmed']
Access and Citation
Cited By Count: 229
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot