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arXiv · 1503.03636

Large Lattice Fractional Fokker-Planck Equation

Vasily E. Tarasov
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Abstract

Equation of long-range particle drift and diffusion on three-dimensional physical lattice is suggested. This equation can be considered as a lattice analogof space-fractional Fokker-Planck equation for continuum. The lattice approach gives a possible microstructural basis for anomalous diffusion in media that are characterized by the non-locality of power-law type. In continuum limit the suggested three-dimensional lattice Fokker-Planck equations give fractional Fokker-Planck equations for continuous media with power-law non-locality that is described by derivatives of non-integer orders. The consistent derivation of the fractional Fokker-Planck equation is proposed as a new basis to describe space-fractional diffusion processes.

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Vasily E. Tarasov. 2015-03-12. Large Lattice Fractional Fokker-Planck Equation. https://doi.org/10.1088/1742-5468%2F2014%2F09%2Fp09036

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