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

2000/01/01 by Eli Barkai, E. Barkai, Ralf Metzler +2 · 8 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy

paper · doi:10.1103/physreve.61.132

openalex publication_date 2000/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

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.

Citations

• Time-Scale Invariance in Transport and Relaxation
• Stochastic Processes in Physics and Chemistry

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• Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications
• Forward and Backward Governing EQuations for Anomalous Diffusion Models Based on the Continuous Time Random Walk
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