Journal of Applied Nonlinear Dynamics
An Analytical Solution for Forcing Nonlinear Fractional Delayed Duffing Oscillator
Journal of Applied Nonlinear Dynamics 10(1) (2021) 111124  DOI:10.5890/JAND.2021.03.007
Yusry O. ElDib
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
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Abstract
Stability analysis of motions in a nonlinear periodically forced, nonlinear
fractional timedelayed, is investigated. An enhanced perturbation method is
developed to study the stability behavior for the nonlinear oscillator. The
basic idea of the method is to apply the annihilator operator to construct a
simplified equation freeness of the periodic force. This method makes the
solution process for the forced problem much simpler. The resulting equation
is valid for studying all types of possible resonance states. The outcome
shows that this alteration method overcomes all shortcomings of the
perturbation method and leads to the very high accuracy of the obtained
solution.
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