2014/10/21 by Afshin Mesbahi, Mohammad Haeri, ءMohammad Haeri +2 · 14 citations
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Fractional Differential Equations Solutions #Fractional calculus #Geometry #Harmonic #Harmonic oscillator #Mathematical analysis #Mathematics #Mathieu function #Mechanical and Optical Resonators #Order (exchange) #Parametric equation #Parametric statistics #Physics #Plane (geometry) #Quantum mechanics
paper · doi:10.1080/00207179.2014.971430
published in International Journal of Control 88(3), 622-630 (Taylor & Francis)
openalex publication_date 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26
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.