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Investigation of complex behaviour of fractal fractional chaotic attractor with mittag-leffler Kernel

Author

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  • Saifullah, Sayed
  • Ali, Amir
  • Franc Doungmo Goufo, Emile

Abstract

This article aims to study the behaviour of a chaotic attractor in the fractal-fractional Mittag-Leffler perspective. The different aspects of the chaotic attractor are observed with different fractal and fractional orders. The existence and uniqueness of the system are presented by using Schauder and Banach fixed point theorems. The stability analysis of the equilibrium points of the system is presented together with Ulam-Hyers stability for the system under consideration. The Lyapunov spectra and the bifurcation in the system with respect to control parameter ζ are studied. The numerical scheme based on the Adam-Bashforth method is established with Lagrangian piecewise interpolation. The complex behaviour of the considered system is numerically illustrated using various fractal and fractional orders. It is observed that, the chaotic attractor self-replicates its pattern in the fractal process when fractal dimension varies.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s096007792100686x
    DOI: 10.1016/j.chaos.2021.111332
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    References listed on IDEAS

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    3. Shojaeizadeh, T. & Mahmoudi, M. & Darehmiraki, M., 2021. "Optimal control problem of advection-diffusion-reaction equation of kind fractal-fractional applying shifted Jacobi polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    Cited by:

    1. Xuan, Liu & Ahmad, Shabir & Ullah, Aman & Saifullah, Sayed & Akgül, Ali & Qu, Haidong, 2022. "Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Rubayyi T. Alqahtani & Shabir Ahmad & Ali Akgül, 2022. "On Numerical Analysis of Bio-Ethanol Production Model with the Effect of Recycling and Death Rates under Fractal Fractional Operators with Three Different Kernels," Mathematics, MDPI, vol. 10(7), pages 1-23, March.

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