Analytical solution of the fractional point-reactor kinetics equations with an external neutron source
In this work, a generalization to fractional order 0 < α ≤ 1 of the point-reactor kinetics equations with an external neutron source is introduced. Using the Laplace transform method, an analytical solution of this problem that is applicable to any time-dependent external neutron source is obtained. The results are applied to the case of an isotopic neutron source. Along with positive reactivity insertion, the presence of this neutron source increases the neutron number density, a condition that is sought during a reactor start-up. The increase is found to be more rapid and evident for lower values of α.