Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach. (8th December 2014)

• Record Type: Journal Article
• Authors: Tarasov, Vasily E.
• Other Names: Lipowski Adam Academic Editor.
• Is Part Of: International journal of statistical mechanics. Volume 2014(2014)
• Publication Date: 2014-12-08
• Subjects: Statistical mechanics -- Periodicals; Statistical mechanics; Periodicals; 530.13
• DOI: 10.1155/2014/873529
• Languages: English
• ISSNs: 2356-7112

Abstract

Abstract : Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of space-fractional diffusion in nonlocal media.