Accelerating and Retarding Anomalous Diffusion

TL;DR

This paper introduces fractional stochastic differential equations driven by Gaussian noise to model and analyze retarding and accelerating anomalous diffusion, exploring their asymptotic behaviors and potential real-world applications.

Contribution

It presents a novel class of fractional stochastic models for retarding and accelerating anomalous diffusion, analyzing their asymptotic properties and providing possible descriptions of such phenomena.

Findings

Derived asymptotic limits of mean squared displacement.

Identified specific cases modeling retarding or accelerating diffusion.

Provided mathematical framework for anomalous diffusion acceleration and retardation.

Abstract

In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe retarding and accelerating subdiffusion and superdiffusion. Short and long time asymptotic limits of the mean squared displacement of the stochastic processes associated with the solutions of these equations are studied. Specific cases of these equations are shown to provide possible descriptions of retarding or accelerating anomalous diffusion.