Distributed-Order Fractional Kinetics

TL;DR

This paper explores various distributed-order fractional kinetic equations to model complex anomalous diffusion processes, including accelerating and decelerating subdiffusion and superdiffusion, expanding the mathematical framework for non-scaling anomalous transport.

Contribution

It introduces different forms of distributed-order fractional kinetic equations and analyzes their effects on various types of anomalous diffusion behaviors.

Findings

Distributed-order equations can model accelerating and decelerating subdiffusion.

Distributed-order equations can also describe accelerating and decelerating superdiffusion.

The study provides a comprehensive framework for complex anomalous diffusion processes.

Abstract

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by distributed-order equations. In the present paper we consider different forms of distributed-order fractional kinetic equations and investigate the effects described by different classes of such equations. In particular, the equations describing accelerating and decelerating subdiffusion, as well as the those describing accelerating and decelerating superdiffusion are presented.