Applying Two Fractional Methods for Studying a Novel General Formula of Delayed-Neutron-Affected Nuclear Reactor Equations

In this work, the novel general formula for a time-dependent nuclear reactor system of equations with delayed neutron effect has been formulated using a fractional calculus model. We explore the properties of this model, including two analytical approximation methods, the Temimi–Ansari method (TAM) and the Sumudu residual power series method (SRPSM), for solving the equation. These methods allow for the computation of approximate solutions at specific points. This is particularly useful for partial differential equations (PDEs) arising in various fields like physics, engineering, and finance. This work is hoped to improve the advancement of nuclear modeling and simulation, providing researchers and engineers with a powerful mathematical tool for studying the complex dynamics of these critical energy systems.