The time-fractional radiative transport equation -- Continuous-time random walk, diffusion approximation, and 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.

References in corpus (3)

• The fundamental solution of the space-time fractional diffusion equation
• A Tutorial on Inverse Problems for Anomalous Diffusion Processes
• Radiative Transport Equation in Rotated Reference Frames