LAUSR

Abstract This work presents a novel solution to Fractional-model equations, it is based on the applying of conformal derivative to fractional calculus and thus obtain a linear multi-term differential equations of integer order (Conformal-model). The main goal of this work is demonstrating the existences of the solutions for the Conformal-model, it is through constraint conditions obtained by the methodology proposed in this work, to analyze and determine the appropriate function to use in its solution and guarantee the stability. The methodology developed is applied to cases with one and six groups of delayed neutrons in abrupt reactivity changes in the reactor, and for the dynamics of startup of PWR nuclear reactor. The results show the main difference of the neutron density behavior among the methods applied to solve the Fractional-model, and against the Classical-model results. Results obtained from Conformal-model are compared against obtained using Fractional-model for different anomalous diffusion coefficient values.