The time-fractional radiative transport equation -- Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

TL;DR

This paper explores the time-fractional radiative transport equation derived from continuous-time random walks, relating it to anomalous diffusion, and solves it using Legendre-polynomial expansion, highlighting its connection to fractional diffusion models.

Contribution

It introduces a derivation of the time-fractional radiative transport equation from continuous-time random walks and demonstrates a solution method using Legendre-polynomial expansion.

Findings

Derivation of the fractional radiative transport equation from random walk models

Connection between the fractional transport equation and anomalous diffusion

Solution of the equation using Legendre-polynomial expansion

Abstract

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.