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 (9): 132 doi: 10.1007/s41365-018-0467-0

• NUCLEAR ENERGY SCIENCE AND ENGINEERING • Previous Articles     Next Articles

Developed mathematical technique for fractional stochastic point kinetics model in nuclear reactor dynamics

Ahmed E. Aboanber 2 • Abdallah A. Nahla 1,2 • Adel M. Edress 2   

  1. 1 Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia
    2 Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
  • Contact: Abdallah A. Nahla
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Ahmed E. Aboanber, Abdallah A. Nahla, Adel M. Edress. Developed mathematical technique for fractional stochastic point kinetics model in nuclear reactor dynamics.Nuclear Science and Techniques, 2018, 29(9): 132     doi: 10.1007/s41365-018-0467-0


Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors, including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations.

Key words: It? stochastic point kinetics equations, Temperature feedback effects, Wiener process, Fractional calculus, Mittage–Leffler function