Fractional delayed damped Mathieu equation

Afshin Mesbahi, Mohammad Haeri, Morad Nazari, Eric A. Butcher

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special cases of the results for the current system.

Original languageEnglish (US)
Pages (from-to)622-630
Number of pages9
JournalInternational Journal of Control
Issue number3
StatePublished - Mar 4 2015


  • Mathieu equation
  • fractional order
  • harmonic balance
  • parametric resonance
  • time delay
  • transition curves

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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