International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2853 2020 2020 Faculty of Science, Zarqa University, Zarqa 13110, Jordan Iqbal Iqbal Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, UAE Iqbal M. Batiha Faculty of Science, Zarqa University, Zarqa 13110, Jordan Mohammed H. E. Abu-Seiā€ Abu-Seiā€™leek Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan Shameseddin Alshorm Laboratory of pure and applied mathematics, University of Mostaganem, Mostaganem 27000, Algeria Amira Abdelnebi Department of Mathematics, Al Zaytoonah University, Amman 11733, Jordan Iqbal H. Jebril Physics Department, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia; Physics Department, Faculty of Women for Arts, Science and Education, Ain Shams University, Cairo 11757, Egypt S. A. Abd El El-Azeem This paper addresses fractional-order versions of multi-group neutron diffusion systems of equations, focusing on two numerical solutions. First, it employs the Laplace transform method to solve the classical version of multi-group neutron diffusion equations. Subsequently, it transforms these equations into their corresponding fractional-order versions using the Caputo differentiator. To handle the resultant fractional-order system, a novel approach is introduced to reduce it from a system of 2Ī±-order to a system of Ī±-order. This converted system is then solved using the so-called Modified Fractional Euler Method (MFEM). As far as we know, this is the first time that such numerical schemes have been used to deal with the systems at hand. The paper covers the multi-group neutron diffusion equations in spherical, cylindrical, and slab reactors, all solved and converted for verification purposes. 2024 2024 08 38 10.54216/IJNS.240401 https://www.americaspg.com/articleinfo/21/show/2853