Constitutive laws for the neutron density current

In this technical note, a fractional wave equation for the average neutron motion in nuclear reactor is considered. This representation covers the full spectrum of the average neutron transport behavior, i.e., Fickian and non-Fickian effects. The fractional diffusion model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional exponent that can be manipulated to obtain the best representation of the neutron transport phenomena. The detrended fluctuation analysis (DFA) method is presented in this paper to estimate the fractional exponent.