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arXiv · 1602.05382

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

Manabu Machida
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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.

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Manabu Machida. 2016-02-17. The time-fractional radiative transport equation -- Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion. https://doi.org/10.1063/1.4973441

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