Original Paper

Nonlinear Dynamics

, Volume 69, Issue 3, pp 721-729

First online:

Hopf bifurcation for a class of fractional differential equations with delay

  • Azizollah BabakhaniAffiliated withFaculty of Basic Science, Babol University of Technology Email author 
  • , Dumitru BaleanuAffiliated withDepartment of Mathematics and Computer Science, Cankaya UniversityInstitute of Space Sciences
  • , Reza KhanbabaieAffiliated withFaculty of Basic Science, Babol University of Technology

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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 calculus Hopf bifurcation