Fractional Langevin equations of distributed order

2010/10/25 by Chai Hok Eab, C. H. Eab, Sungbin Lim +1
Mathematics · Medicine · Physics and Astronomy · #Anomalous diffusion #Computer science #Diffusion #Displacement (psychology) #Exponent #Fractional Differential Equations Solutions #Geometry #Langevin dynamics #Langevin equation #Logarithm #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Mean squared displacement #Nonlinear Differential Equations Analysis #Order (exchange) #Physics #Quantum mechanics #Scaling #Statistical physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.83.031136

published as Physical Review E 83, 031136 (2011) · 10 pages, 2 figures

arxiv created 2010/10/25 · openalex publication_date 2011/03/29 · arxiv updated 2012/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Distributed-order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be used to model the kinetics of retarding subdiffusion whose scaling exponent decreases with time and the strongly anomalous ultraslow diffusion with mean square displacement which varies asymptotically as a power of logarithm of time.

Citations

• Tauberian Theory
• Statistical and dynamical properties of the discrete Sinai model at finite times
• Fractional Fokker-Planck equation for ultraslow kinetics
• Multifractal random walk
• Ultraslow vacancy-mediated tracer diffusion in two dimensions: The Einstein relation verified
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• Linear Models of Dissipation whose Q is almost Frequency Independent--II
• Fractional Differential Equations