The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1847–1856 | Cite as

Fractional Fokker-Planck equation for anomalous diffusion in a potential: Exact matrix continued fraction solutions

  • W. T. Coffey
  • Y. P. KalmykovEmail author
  • S. V. Titov
Regular Article


Methods for the exact solution of fractional Fokker-Planck equations for anomalous diffusion in an external potential are discussed using both ordinary and matrix continued fractions, whereby the scalar multi-term recurrence relations generated by such fractional diffusion equations are reduced to three-term matrix ones. The procedure is illustrated by solving various problems concerning the anomalous translational diffusion in both periodic and double-well potentials.


Recurrence Relation European Physical Journal Special Topic Continue Fraction Continuous Time Random Walk Term Recurrence Relation 
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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Department of Electronic and Electrical EngineeringTrinity CollegeDublin 2Ireland
  2. 2.Laboratoire de Mathmatiques et de PhysiqueUniv. Perpignan, via DomitiaPerpignanFrance
  3. 3.Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of SciencesFryazino, Moscow RegionRussia

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