Nonlinear Dynamics

, Volume 69, Issue 3, pp 721–729

Hopf bifurcation for a class of fractional differential equations with delay

  • Azizollah Babakhani
  • Dumitru Baleanu
  • Reza Khanbabaie
Original Paper

DOI: 10.1007/s11071-011-0299-5

Cite this article as:
Babakhani, A., Baleanu, D. & Khanbabaie, R. Nonlinear Dyn (2012) 69: 721. doi:10.1007/s11071-011-0299-5


The main purpose of this manuscript is to prove the existence of solutions for delay fractional order differential equations (FDE) at the neighborhood of its equilibrium point. After we convert the delay FDE into linear delay FDE by using its equilibrium point, we define the 1:2 resonant double Hopf point set with its characteristic equation. We find the members of this set in different cases. The bifurcation curves for a class of delay FDE are obtained within a differential operator of Caputo type with the lower terminal at −∞.


Fractional calculusHopf bifurcation

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Azizollah Babakhani
    • 1
  • Dumitru Baleanu
    • 2
    • 3
  • Reza Khanbabaie
    • 1
  1. 1.Faculty of Basic ScienceBabol University of TechnologyBabolIran
  2. 2.Department of Mathematics and Computer ScienceCankaya UniversityAnkaraTurkey
  3. 3.Institute of Space SciencesMagurele-BucharestRomania