Discontinuity, Nonlinearity, and Complexity
Stability Approach of a FractionalDelayed Duffing Oscillator
Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 367376  DOI:10.5890/DNC.2020.09.003
Yusry O. ElDib
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
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Abstract
In this proposal, a formulation for the approximateanalytical solution of a fractionaldelayed damping Duffing oscillator is developed. The fractional derivative is established using the RiemannLiouville definition. In this scheme, the solution used a homotopy perturbation. In this proposal, a transcendental frequency equation is established. Finally, an analytic solution to the complicated algebraic frequency equation is obtained. Stability conditions are formulated to maintain the structure of the oscillatory solution.
The case of undelayed damping Duffing equation is investigated through the modified homotopy technique which is assumed to be the successor to obtain the solution.
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