The radiative transport equation with waiting time and its diffusion approximation with a time-fractional derivative

TL;DR

This paper derives a time-fractional advection-diffusion equation from the radiative transport equation with waiting time, providing a new mathematical model for anomalous underground particle diffusion.

Contribution

It introduces a novel derivation of a fractional diffusion equation from the radiative transport framework incorporating waiting time effects.

Findings

Derivation of a fractional diffusion equation from radiative transport with waiting time

Provides a new mathematical model for anomalous underground particle transport

Bridges radiative transport and fractional diffusion theories

Abstract

Albeit the past intensive research, the governing equation of anomalous diffusion which is observed for the transport of particles underground is still an open problem. In this paper, as a governing equation, the advection-diffusion equation with a time-fractional derivative term is derived from the radiative transport equation with an integral term for waiting time.