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<p>The Lorenz system is known for its sensitivity to initial conditions. A small variation in the initial conditions gives drastically different trajectories over time. The Lorenz system is a classic example of deterministic chaos whose random and complex behavior emerges from deterministic equations. This work focuses on the dynamical behavior of the 5-Dimensional Mittag-Leffler-Fractal-Fractional order Lorenz system. The detailed proof for the existence of a solution with uniqueness is obtained. The chaotic nature of the system is verified using Lyapunov exponents and Poincare sections. The solutions are found numerically. Lastly, the dynamical behavior is represented for distinct fractal-fractional order.</p>

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Investigating Chaos in the Lorenz System based on Fractal-Fractional Derivatives

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月7日

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  • Ghaliah Alhamzi,
  • Shivani Sharma,
  • Dumitru Baleanu,
  • Ravi Shanker Dubey

摘要

The Lorenz system is known for its sensitivity to initial conditions. A small variation in the initial conditions gives drastically different trajectories over time. The Lorenz system is a classic example of deterministic chaos whose random and complex behavior emerges from deterministic equations. This work focuses on the dynamical behavior of the 5-Dimensional Mittag-Leffler-Fractal-Fractional order Lorenz system. The detailed proof for the existence of a solution with uniqueness is obtained. The chaotic nature of the system is verified using Lyapunov exponents and Poincare sections. The solutions are found numerically. Lastly, the dynamical behavior is represented for distinct fractal-fractional order.