Space-fractional neutron diffusion equation with Riesz fractional derivative

Abstract

Space-fractional neutron diffusion equation with Riesz fractional derivative of order 1 < α ≤ 2 is applied to well-known problems in neutron physics such as the one-group and two-group approximations of neutron diffusion from an infinite planar source. Using the Fourier-transform method, the corresponding neutron fluxes are derived and expressed in terms of Fox's H-function. Graphical representations of the neutron flux show that its maximum shifts upward in the fractional regime and deviates further from the non-fractional one (i.e., when α=2) as α decreases.