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From continuous time random walks to the fractional Fokker-Planck equation

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 2000 · Vol. 61(1) · pp. 132–138

Eli Barkai✉(Massachusetts Institute of Technology)Ralf Metzler(Tel Aviv University)J. Klafter(Tel Aviv University)

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Abstract

We generalize the continuous time random walk (CTRW) to include the effect of space dependent jump probabilities. When the mean waiting time diverges we derive a fractional Fokker-Planck equation (FFPE). This equation describes anomalous diffusion in an external force field and close to thermal equilibrium. We discuss the domain of validity of the fractional kinetic equation. For the force free case we compare between the CTRW solution and that of the FFPE.

Fractional Differential Equations Solutions Statistical Mechanics and Entropy Advanced Thermodynamics and Statistical MechanicsContinuous-time random walkFokker–Planck equationStatistical physicsRandom walkPhysicsAnomalous diffusionJumpDiffusion equationHeterogeneous random walk in one dimensionLévy flight

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