Fractional Langevin Equation of Distributed Order

TL;DR

This paper introduces distributed order fractional Langevin equations to model complex anomalous diffusion behaviors, including retarding subdiffusion and ultraslow diffusion, capturing variable scaling exponents over time.

Contribution

It presents a novel class of fractional Langevin equations of distributed order for modeling complex anomalous diffusion phenomena.

Findings

Modeling of retarding subdiffusion with decreasing scaling exponent

Description of ultraslow diffusion with logarithmic mean square displacement

Application of distributed order equations to complex diffusion processes

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.