  We establish asymptotic diffusion limits of the non-classical transport
equation derived in [E. W. Larsen, A generalized Boltzmann equation for
non-classical particle transport, Joint international topical meeting on
mathematics & computation and supercomputing in nuclear applications, 2007]. 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 uses the Fourier transform combined with
a moment method. We conclude with remarks on the diffusion limit of the
periodic Lorentz gas equation.
