https://doi.org/10.1140/epjst/e2013-01968-x
Regular Article
Fractional Fokker-Planck equation for anomalous diffusion in a potential: Exact matrix continued fraction solutions
1 Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland
2 Univ. Perpignan, via Domitia, Laboratoire de Mathmatiques et de Physique, EA 4217, 66860 Perpignan, France
3 Kotelnikov Institute of Radio Engineering and Electronics of the Russian Academy of Sciences, Vvedenskii Square 1, Fryazino, Moscow Region 141120, Russia
a e-mail: kalmykov@univ-perp.fr
Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013
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.
© EDP Sciences, Springer-Verlag, 2013
