A novel fractional technique for the modified point kinetics equations

Abstract

A fractional model for the modified point kinetics equations is derived and analyzed. An analytical method is used to solve the fractional model for the modified point kinetics equations. This methodical technique is based on the representation of the neutron density as a power series of the relaxation time as a small parameter. The validity of the fractional model is tested for different cases of step, ramp and sinusoidal reactivity. The results show that the fractional model for the modified point kinetics equations is the best representation of neutron density for subcritical and supercritical reactors.

Keywords

• Point kinetics equations
• Multi-group of delayed neutrons
• Relaxation time effects
• Riemann–Liouville definition
• Fractional calculus