Numerical-analytical solutions of the fractional point kinetic model with Caputo derivatives

Abstract

Novel solutions to the fractional neutron point kinetic equations in terms of Caputo derivatives are obtained for three different cases: 1) constant reactivity; 2) cold startup process of a Pressurized Water Reactor; and 3) start-up of a nuclear reactor. Numerical-analytical solutions for the first and second cases are achieved via Laplace transform technique with Talbot's method for the numerical inversion of the transformed equations. Analytical solutions for the third case are constructed by a collocation method using Chebyshev polynomials. The solutions predict inertia effects observed as a growth in neutron density up to reaching a peak and then a gradual decrease followed by a series of oscillations until reaching a steady state. This behavior, on the one hand, is accentuated as the fractional order decreases, and on the other hand, it is reconciled with the fact that the propagation speed of the neutrons within the reactor is finite.