Development and Analysis of Fractional-order Neutron Telegraph Equation

Abstract

This chapter starts with the motivation to model neutron movement as anomalous diffusion, particularly subdiffusion, and then presents the derivation of the fractional-order neutron telegraph model using the stochastic framework of continuous-time random walk. Its longtime and short-time behaviors are analyzed. The mean-squared displacement of various transport models is calculated, and the comparative study is carried out. Finally, all the integer-order and fractional-order partial differential equation models are solved using separation of variables method to study the spatial distribution and time evolution of neutron flux in the slab reactor.