2003/01/24 by A. V. Chechkin, A. V Chechkin, J. Klafter +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Diffusion #Diffusion equation #Displacement (psychology) #Exponent #Fractional Differential Equations Solutions #Logarithm #Order (exchange) #Position (finance) #Power (physics) #cond-mat.dis-nn #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1209/epl/i2003-00539-0
arxiv created 2003/01/24 · openalex publication_date 2003/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Several classes of physical systems exhibit ultraslow diffusion for which the mean-squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability distribution of particle's position at long times is a double-sided exponential. We show that such behaviors can be adequately described by a distributed-order fractional Fokker-Planck equations with a power law weighting function. We discuss the equations and the properties of their solutions, and connect this description with a scheme based on continuous-time random walks.