Numerical Solutions for Fractional Multi-Group Neutron Diffusion System of Equations

This paper addresses fractional-order versions of multi-group neutron diffusion systems of equations, focusing on two numerical solutions. First, it employs the Laplace transform method to solve the classical version of multi-group neutron diffusion equations. Subsequently, it transforms these equations into their corresponding fractional-order versions using the Caputo differentiator. To handle the resultant fractional-order system, a novel approach is introduced to reduce it from a system of 2α-order to a system of α-order. This converted system is then solved using the so-called Modified Fractional Euler Method (MFEM). As far as we know, this is the first time that such numerical schemes have been used to deal with the systems at hand. The paper covers the multi-group neutron diffusion equations in spherical, cylindrical, and slab reactors, all solved and converted for verification purposes.