Operator solutions for fractional Fokker-Planck equations

Abstract

We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators.

4 pages, 3 figures

References in corpus (5)

• Exact and explicit probability densities for one-sided Levy stable distributions
• Fractional diffusion equations and processes with randomly varying time
• Levy stable two-sided distributions: exact and explicit densities for asymmetric case
• Relativistic equations with fractional and pseudo-differential operators
• Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions

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