Fractional Langevin Equation of Distributed Order

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 asymptoically as a power of logarithm of time.

10 pages, 2 figures

References in corpus (12)

• A multifractal random walk
• Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations
• Distributed Order Calculus and Equations of Ultraslow Diffusion
• Fractional Fokker-Planck Equation for Ultraslow Kinetics
• Fractional Diffusion Equation for a Power-Law-Truncated Levy Process
• Multifractal random walk in copepod behavior
• Fractional generalized Langevin equation approach to single-file diffusion
• Ultra-Slow Vacancy-Mediated Tracer Diffusion in Two Dimensions: The Einstein Relation Verified
• Anomalous Diffusion in Aperiodic Environments
• Modeling Single-File Diffusion by Step Fractional Brownian Motion and Generalized Fractional Langevin Equation
• Anomalous diffusion and dynamical localization in a parabolic map
• Statistical and dynamical properties of the discrete Sinai model at finite times

Cited by in corpus (15)

• Distributed-order fractional Cauchy problems on bounded domains
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Subdiffusion equation with Caputo fractional derivative with respect to another function
• Accelerating and Retarding Anomalous Diffusion
• Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
• Empirical observations of ultraslow diffusion driven by the fractional dynamics in languages: Dynamical statistical properties of word counts of already popular words
• Petrov-Galerkin Method for Fully Distributed-Order Fractional Partial Differential Equations
• Boundary conditions at a thin membrane for normal diffusion equation which generate subdiffusion
• An Alternating Direction Explicit Method for Time Evolution Equations with Applications to Fractional Differential Equations
• Critical dynamics in systems controlled by fractional kinetic equations
• Langevin equation and fractional dynamics
• Anomalous Translational Dynamics of Molecular Probes Near the Polymer Glass Transition
• Numerical algorithm for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term
• Deterministic and stochastic analysis of distributed order systems using operational matrix
• Relations between anomalous diffusion and fluctuation scaling: The case of ultraslow diffusion and time-scale-independent fluctuation scaling in language