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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Stability Approach of a Fractional-Delayed Duffing Oscillator

Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 367--376 | DOI:10.5890/DNC.2020.09.003

Yusry O. El-Dib

Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt

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Abstract

In this proposal, a formulation for the approximate-analytical solution of a fractional-delayed damping Duffing oscillator is developed. The fractional derivative is established using the Riemann-Liouville 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 un-delayed 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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