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A new nonlinear duffing system with sequential fractional derivatives

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  • Bezziou, Mohamed
  • Jebril, Iqbal
  • Dahmani, Zoubir

Abstract

By considering the Caputo fractional derivative and Riemann-Liouville integral, in the present work, we are concerned with a nonlinear sequential fractional differential system of Duffing oscillator type. The considered system has neither the commutativity nor the semi group properties, since the sum of the two orders of derivatives, of the left hand side of the problem, are outside the interval [0,1]. With the absence of these two properties, we have to find other arguments to obtain the integral representation of the problem, to be able thereafter to present the other main results. Then, using the contraction mapping principle and Scheafer theorem, two main theorems on the uniqueness and existence of solutions are proved. Finally, some examples are given to illustrate the proposed main results.

Suggested Citation

  • Bezziou, Mohamed & Jebril, Iqbal & Dahmani, Zoubir, 2021. "A new nonlinear duffing system with sequential fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006019
    DOI: 10.1016/j.chaos.2021.111247
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    References listed on IDEAS

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    1. Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    2. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Dokuyucu, Mustafa Ali & Dutta, Hemen, 2020. "A fractional order model for Ebola Virus with the new Caputo fractional derivative without singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
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    Cited by:

    1. Zhao, Jiahao & Sun, Hanyu & Zhang, Xiaofang & Han, Xiujing & Han, Meng & Bi, Qinsheng, 2024. "Frequency switching leads to distinctive fast–slow behaviors in Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    2. Alvaro H. Salas & Ma’mon Abu Hammad & Badriah M. Alotaibi & Lamiaa S. El-Sherif & Samir A. El-Tantawy, 2022. "Closed-Form Solutions to a Forced Damped Rotational Pendulum Oscillator," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    3. Amira Abdelnebi & Zoubir Dahmani, 2022. "New Van der Pol–Duffing Jerk Fractional Differential Oscillator of Sequential Type," Mathematics, MDPI, vol. 10(19), pages 1-16, September.

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