In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are typically heavy-tailed distributions, but also classical Gaussian equilibrium distributions allow for this phenomena if combined with a degenerate collision freq...

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the spatial homogenous boundary conditions. This is then used to solve time-fractional diffusion equation spectrally. The elements all spectral matrices are explicitly obtained in terms Gauss hypergeometric function. convergence error analysis proposed expansion studied. Numerical results indicate high accurac...