Abstract
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.
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Coffey, W.T., Kalmykov, Y.P. & Titov, S.V. Fractional Fokker-Planck equation for anomalous diffusion in a potential: Exact matrix continued fraction solutions. Eur. Phys. J. Spec. Top. 222, 1847–1856 (2013). https://doi.org/10.1140/epjst/e2013-01968-x
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DOI: https://doi.org/10.1140/epjst/e2013-01968-x