2014/10/21 by Afshin Mesbahi, Mohammad Haeri, ءMohammad Haeri +2 · 1 citation
Physics and Astronomy · Mathematics · #Mechanical and Optical Resonators #Fractional Differential Equations Solutions #Advanced Fiber Laser Technologies
paper · doi:10.1080/00207179.2014.971430
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.