# Nuclear Science and Techniques

《核技术》(英文版) ISSN 1001-8042 CN 31-1559/TL     2019 Impact factor 1.556

Nuclear Science and Techniques ›› 2018, Vol. 29 ›› Issue (1): 14

• NUCLEAR ENERGY SCIENCE AND ENGINEERING •

### Spectrum behavior for the nonlinear fractional point reactor kinetics model

Ahmed E. Aboanber, Abdallah A. Nahla, A.A. Hemeda

1. Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
• Contact: Ahmed E. Aboanber E-mail:ahmed.aboanber@science.tanta.edu.eg
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Ahmed E. Aboanber, Abdallah A. Nahla, A.A. Hemeda. Spectrum behavior for the nonlinear fractional point reactor kinetics model.Nuclear Science and Techniques, 2018, 29(1): 14
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Abstract:

The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons, which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor’s formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error (local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes.