Analysis of fractional-order telegraph model for neutron transport in nuclear reactor with slab geometry

This paper deals with the analysis of fractional-order (FO) telegraph equation which models the transport of thermal neutrons inside a nuclear reactor with slab geometry. The FO model, previously developed by the authors, models the neutron transport as anomalous diffusion, precisely a sub-diffusion. This model removes the lacunae of the conventional integer-order model of neutron movements. Here, the FO model is solved using the well known technique of separation of variables and the spatial distribution and time evolution of the neutron flux in the slab reactor are computed. This exercise is probably being performed for the first time for the fractional-order model of neutron transport. It clearly depicts the wave-like nature of the neutron flux. Also, the convergence of neutron flux for FO telegraph and subdiffusion models for asymptotic time establishes the long-time subdiffusive behaviour of the FO telegraph equation. The analysis carried out in this paper is thus forms a crucial step in the process of development of fractional-order model for a nuclear reactor.