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Mathematical Problems in Engineering
Volume 2017, Article ID 6714538, 12 pages
Research Article

Fractional-Order Model of Two-Prey One-Predator System

1Mathematics Department, Faculty of Sciences, King Khalid University, Abha 9004, Saudi Arabia
2Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3Mathematics Department, Faculty of Sciences and Arts, King Khalid University, Dhahran Al Janoub, Saudi Arabia
4Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt

Correspondence should be addressed to Ahlam Abdullah Al-Raezah; moc.liamtoh@1102-hmoooolh

Received 13 April 2017; Revised 22 June 2017; Accepted 30 July 2017; Published 30 August 2017

Academic Editor: Ben T. Nohara

Copyright © 2017 Mohammed Fathy Elettreby et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a fractional-order model of the interaction within two-prey and one-predator system. We prove the existence and the uniqueness of the solutions of this model. We investigate in detail the local asymptotic stability of the equilibrium solutions of this model. Also, we illustrate the analytical results by some numerical simulations. Finally, we give an example of an equilibrium solution that is centre for the integer order system, while it is locally asymptotically stable for its fractional-order counterpart.