Solving a Novel System of Time-Dependent Nuclear Reactor Equations of Fractional Order

Abstract

Building upon the previous research that solved neutron diffusion equations in simplified slab geometry, this study advances the field by addressing the more complex cylindrical geometry, focusing on neutron diffusion equations that are coupled with delayed neutrons in cylindrical reactors of fractional order. The method of solving used integrates the technique of residual power series (RPS) with the Laplace transform (LT) method. Anomalous neutron behavior is explained by examining the non-Gaussian scenario with various fractional parameters α. The LRPSM Laplace transform and residual power series method employed in this approach eliminates the complex difficulties. This simplicity makes the method particularly coherent with different fractional calculus applications. To validate the proposed method, numerical simulations are conducted with two different initial conditions representing distinct scenarios. The obtained results are presented in suitable tables and figures. It should be emphasized that this system is solved for the first time utilizing fractional calculus techniques. The outcomes are consistent with those achieved using the Adomian decomposition method.