Modified multiple scale technique for the stability of the fractional delayed nonlinear oscillator

In the present proposal, the familiar method of the parameter expansion is combined with the multiple scales to study the stability behaviour of the Riemann-Liouville fractional derivative applied to the cubic delayed Duffing oscillator. The analysis of the modified multiple scale perturbation leads to a system of nonlinear differential-algebraic equations governing the solvability conditions. The nonlinear differential equation was reduced to the linear differential equation with the help of the algebraic one. The stability attitude of the periodic motion is determined by the steady-state analysis. Such a periodic motion is needed to better understand the dynamics of the fractional cubic delayed Duffing oscillator.