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Journal of Applied Nonlinear Dynamics 10(1) (2021) 111--124 | DOI:10.5890/JAND.2021.03.007

Yusry O. El-Dib

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 time-delayed, 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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