The paper presents the results concerning numerical solutions of the fractional point kinetics and heat exchange model for nuclear reactor. The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and numerical solutions were proposed. Mathematical model has been implemented in the Matlab environment and tested using typical step input change. The analysis of the impact of chosen parameters was conducted.


fractional calculus; fission reactors; differential equations

Anglart H.: Nuclear Reactor Dynamics and stability. Instytut Techniki Cieplnej Politechniki Warszawskiej, 2013.

Ackermann G.: Eksploatacja elektrowni jądrowych. WNT, Warszawa 1987.

Baum G., Duzinkiewicz K.: Model symulacyjny jednowymiarowej dynamiki reaktora typu WWER-440 (kinetyka, zagadnienia cieplno-przepływowe). Raport. Instytut Elektroenergetyki i Automatyki, Politechnika Gdańska, 1989.

Caponetto R., Dongola G., Fortuna L., Petras I.: Fractional order systems. Modelling and Control Applications. World Scientific Series of Nonlinear Science, Series A, Vol. 72, 2010.

Chen Y.Q.: Fractional Calculus, Delay Dynamics and Networked Control Systems. Resilient Control Systems (ISRCS), 2010.

Duderstadt J.J., Hamilton L.J.: Nuclear Reactor Analysis. John Wiley & Sons, Inc., New York, 1942.

Duzinkiewicz K., Baum G., Michalak A.: Model symulacyjny podstawowych procesów dynamicznych reaktora typu WWER oparty o modele o parametrach skupionych. Raporty. Instytut Elektroenergetyki i Automatyki, Politechnika Gdańska, 1989.

Espinosa-Paredes G., Polo-Labbarios M., Espinosa-Martinez E., del Valle-Gallegos E.: Fractional neutron point kinetics equations for nuclear reactor dynamics. Annals of Nuclear Energy 38, 2011, s. 307-330.

Maiti D., Janarthanan R., Konar A.: Complete Identification of a Dynamic Fractional Order System Under Non-ideal Conditions Using Fractional Differintegral Definitions. Department of Eletronics and Telecommunication Engineering, 2008.

Petras I.: Fractional-Order Nonlinear Systems. Modelling, Analysis and Simulation. Springer, New York, 2011.

Podlubny I.: Fractional Differential Equations. Academic Press, San Diego, 1999.

Schultz M. A.: Control of Nuclear reaktors and Power Plants. McGew-Hill book Company, Inc. New York, 1961.

Published : 2014-03-12

Nowak, T. K., & Duzinkiewicz, K. (2014). FRACTIONAL MODEL OF FAST PROCESSES IN NUCLEAR REACTOR ANALYSIS. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 4(1), 44-47.

Tomasz Karol Nowak
Poznan University of Technology  Poland
Kazimierz Duzinkiewicz 
Poznan University of Technology  Poland