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Analysis Of Hidden Attractors Of Non-Equilibrium Fractal-Fractional Chaotic System With One Signum Function

Author

Listed:
  • LEI ZHANG

    (Department of Mathematics, Hanshan Normal University, Chaozhou 521041 P. R. China)

  • SHABIR AHMAD

    (Department of Mathematics, University of Malakand, Chakdara Dir (L), 18800, Khyber Pakhtunkhwa, Pakistan)

  • AMAN ULLAH

    (Department of Mathematics, University of Malakand, Chakdara Dir (L), 18800, Khyber Pakhtunkhwa, Pakistan)

  • ALI AKGÃœL

    (Department of Mathematics, Art and Science Faculty, Siirt University, TR-56100 Siirt, Turkey)

  • ESRA KARATAS AKGÃœL

    (Department of Mathematics, Art and Science Faculty, Siirt University, TR-56100 Siirt, Turkey)

Abstract

In 2017, Atangana proposed more generalized operators depending on two parameters: one is fractional order (FO) and other is fractal dimension. The novel operators are defined with three different kernels. These operators produced excellent dynamics of the chaotic systems. In this paper, the Caputo fractal-fractional operator is used to explore a chaotic system which contains only one signum function. The existence theory is developed by using the fixed-point result of Leray–Schauder to prove that the considered chaotic system possesses at least one solution. The proposed chaotic system has a unique solution, according to Banach’s fixed-point theorem. We demonstrate that the suggested chaotic system is Ulam–Hyres (UH) stable under the novel operator of power law kernel by employing nonlinear functional analysis. The Adams–Bashforth technique is used to evaluate the numerical outcomes of the considered model. We show the complex structure of numerical solutions for different FO and fractal dimension values.

Suggested Citation

  • Lei Zhang & Shabir Ahmad & Aman Ullah & Ali Akgãœl & Esra Karatas Akgãœl, 2022. "Analysis Of Hidden Attractors Of Non-Equilibrium Fractal-Fractional Chaotic System With One Signum Function," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-16, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401399
    DOI: 10.1142/S0218348X22401399
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    Cited by:

    1. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. John Venetis, 2024. "An Explicit Form of Signum Function," Mathematics, MDPI, vol. 12(20), pages 1-10, October.

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