# American Institute of Mathematical Sciences

December  2018, 11(6): 1503-1526. doi: 10.3934/krm.2018059

## Fractional diffusion limits of non-classical transport equations

 1 Karlsruhe Institute of Technology, Steinbuch Center for Computing, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany 2 Dept. of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada

* Corresponding author: Martin Frank

Received  July 2017 Revised  October 2017 Published  June 2018

Fund Project: The first author is supported by the German research foundation DFG under grant FR2841/6-1

We establish asymptotic diffusion limits of the non-classical transport equation derived in [12]. By introducing appropriate scaling parameters, the limits will be either regular or fractional diffusion equations depending on the tail behaviour of the path-length distribution. Our analysis is based on a combination of the Fourier transform and a moment method. We put special focus on dealing with anisotropic scattering, which compared to the isotropic case makes the analysis significantly more involved.

Citation: Martin Frank, Weiran Sun. Fractional diffusion limits of non-classical transport equations. Kinetic & Related Models, 2018, 11 (6) : 1503-1526. doi: 10.3934/krm.2018059
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