Analytical solution of the fractional point kinetics equations with multi-group of delayed neutrons during start-up of a nuclear reactor

An analytical solution of the fractional model of the stiff point kinetics equations with multi-group of delayed neutrons is presented during a start-up of a nuclear reactor. The reactor start-up is a process of reactivity insertion which is mainly carried out by lifting control rods discontinuously. The inserting reactivity is a linear through the reactor start-up time and a constant after that. The analytical solution is based on the prompt jump approximation during a reactor start-up time and Laplace transform method otherwise that time. The response of neutron density is calculated for the ordinary and fractional models of the point kinetics equations with six groups of delayed neutrons. The results of neutron density for different fractional orders are performed and compared with the results of ordinary model. The comparison shows that the proposed analytical solution agrees well with the Zhang analytical method for the ordinary model with average one group of delayed neutrons. This agreement is decreasing in the case of six groups of delayed neutrons. In addition, the relations of the neutron density with the speed of lifting control rods and the fractional order are discussed.