<![CDATA[This study addresses the critical need for accurate neutron diffusion modeling in cylindrical reactors, focusing on the two-energy groups neutron diffusion system. Such modeling is essential for optimizing reactor design and safety in nuclear engineering. The research primarily aims to enhance computational methods by transitioning from a traditional integer-order model to a more sophisticated fractional-order model, which can capture complex physical phenomena with greater precision. The study employs the Laplace Transform Method (LTM) to first solve the integer-order system and then extends this approach to a fractional-order system using the Caputo derivative, a method well-suited for systems with memory effects. To efficiently solve the resulting fractional-order model, we introduce the Modified Fractional Euler Method (MFEM), designed to improve numerical accuracy and stability. The effectiveness of this approach is demonstrated through specific numerical applications, such as simulating neutron flux distributions, which validate the model’s accuracy and its potential impact on advancing reactor physics. These applications showcase the practical relevance of the proposed methods and their contribution to improving nuclear reactor simulations.]]>
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