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Anomalous Diffusion by the Fractional Fokker-Planck Equation and Lévy Stable Processes

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Fractional Dynamics, Anomalous Transport and Plasma Science

Abstract

The work presented here is a review of current developments in modelling anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution as solutions to the Fokker-Planck equation and is compared to results from Langevin simulations. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics.

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Acknowledgements

The author would like to acknowledge contributions and fruitful discussions with Dr. E. Kim and Dr. D. del-Castillo-Negrete.

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Authors and Affiliations

  1. Department of Space, Earth and Environment, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Johan Anderson

  2. Laboratory for Plasma Physics - LPP-ERM/KMS, Royal Military Academy, 1000, Brussels, Belgium

    Sara Moradi

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  1. Johan Anderson
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  2. Sara Moradi
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Correspondence to Johan Anderson .

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Editors and Affiliations

  1. ManLab, Technical University of Crete, Chania, Crete, Greece

    Christos H. Skiadas

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Anderson, J., Moradi, S. (2018). Anomalous Diffusion by the Fractional Fokker-Planck Equation and Lévy Stable Processes. In: Skiadas, C. (eds) Fractional Dynamics, Anomalous Transport and Plasma Science. Springer, Cham. https://doi.org/10.1007/978-3-030-04483-1_4

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