On the numerical solution of the neutron fractional diffusion equation

• The new version of neutron diffusion equation which established on the fractional derivatives is presented.
• The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame.
• NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators.
• The results show that “Keff” strongly depends on the order of fractional derivative.

In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (Keff) depends strongly on the order of fractional derivative.