A fractional Fokker-Planck model for anomalous diffusion

Johan Anderson, Eun Jin Kim, Sara Moradi

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21 Citations (Scopus)
16 Downloads (Pure)


In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.

Original languageEnglish
Article number122109
JournalPhysics of Plasmas
Issue number12
Publication statusPublished - 16 Dec 2014
Externally publishedYes

Bibliographical note

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Anderson, J, Kim, EJ & Moradi, S 2014, 'A fractional Fokker-Planck model for anomalous diffusion' Physics of Plasmas, vol. 21, no. 12, 122109 and may be found at https://dx.doi.org/10.1063/1.4904201URL/link for published article abstract.

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.


  • Anomalous Diffusion
  • Fractional Fokker-Planck Equation
  • Self-Organisation

ASJC Scopus subject areas

  • Condensed Matter Physics


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