Using Laplace Residual Power Series Method in Solving Coupled Fractional Neutron Diffusion Equations with Delayed Neutrons System

Abstract

In this paper, a system of coupled fractional neutron diffusion equations with delayed neutrons was solved efficiently by using a combination of residual power series and Laplace transform techniques, and the anomalous diffusion was considered by taking the non-Gaussian case with different values of fractional parameter α. The Laplace residual power series method (LRPSM) does not require differentiation, conversion, or discretization for the assumed conditions, so the approach is simple and suitable for solving higher-order fractional differential equations. To assure the theoretical results, two different neutron flux initial conditions were presented numerically, where the needed Mathematica codes were performed using essential nuclear reactor cross-section data, and the results for different values of times were tabulated and graphically figured out. Finally, it must be noted that the results align with the Adomian decomposition method.

Keywords

• diffusion equation
• kinetic point equation
• Laplace residual power series
• fractional calculus