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On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory

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  • Ávalos-Ruiz, L.F.
  • Gómez-Aguilar, J.F.
  • Atangana, A.
  • Owolabi, Kolade M.

Abstract

In this paper, we propose a fractional form of two-dimensional generalized mythical bird, butterfly wings and paradise bird maps involving the fractional conformable derivative of Khalil’s and Atangana’s type, the Liouville–Caputo and Atangana–Baleanu derivatives with constant and variable-order. We obtain new chaotical behaviors considering numerical schemes based on the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. Also, the dynamics of the proposed maps are investigated numerically through phase plots considering combinations of these derivatives and mixed integration methods for each map. The numerical simulations show very strange and new behaviors for the first time in this manuscript.

Suggested Citation

  • Ávalos-Ruiz, L.F. & Gómez-Aguilar, J.F. & Atangana, A. & Owolabi, Kolade M., 2019. "On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 364-388.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:364-388
    DOI: 10.1016/j.chaos.2019.07.010
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    Cited by:

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    3. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Saifullah, Sayed & Ali, Amir & Franc Doungmo Goufo, Emile, 2021. "Investigation of complex behaviour of fractal fractional chaotic attractor with mittag-leffler Kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Ullah, Malik Zaka & Mallawi, Fouad & Baleanu, Dumitru & Alshomrani, Ali Saleh, 2020. "A new fractional study on the chaotic vibration and state-feedback control of a nonlinear suspension system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

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