This paper provides a novel approach to studying the chaos control and synchronization of fractional-order hybrid Darcy–Brinkman systems (FOHDBs). We use the truncated Galerkin method to transform the system of partial differential equations (PDEs) into ordinary differential equations (ODEs) based on Fourier modes in a nonlinear low-dimensional Brinkman model. In the nonlinear complex system, hybrid nanoparticles and fluid flow physical characteristics are considered to be external disturbances. As a result, the implications of model uncertainty and external disruptions are fully absorbed into the problem, further complicating it and resulting in highly complex and unpredictable behaviors. In addition, To assure the occurrence of the sliding motion in a finite amount of time, an appropriate robust fractional sliding mode technique is proposed. Sliding motion is shown to occur in finite time using the fractional Lyapunov stability. Following that, we discussed control techniques for achieving infinitesimally close to an equilibrium of chaotic states and tracking errors. It is important to note that FOHDBs and external stochastic disturbances can be controlled using the proposed fractional nonsingular terminal sliding mode control technique. Finally, the effectiveness and applicability of the suggested finite-time control technique are graphically illustrated by the analytical and numerical simulations.

中文翻译：

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通过滑模控制对分数阶非自主混合非线性复杂系统进行有限时间混沌稳定和同步的随机扰动


本文提供了一种研究分数阶混合达西-布林克曼系统（FOHDB）的混沌控制和同步的新方法。我们使用截断伽辽金方法将偏微分方程组 (PDE) 转换为基于非线性低维 Brinkman 模型中傅里叶模式的常微分方程 (ODE)。在非线性复杂系统中，混合纳米颗粒和流体流动物理特性被认为是外部扰动。因此，模型不确定性和外部干扰的影响被完全吸收到问题中，使问题进一步复杂化，并导致高度复杂和不可预测的行为。此外，为了确保在有限时间内发生滑动运动，提出了一种适当的鲁棒分数滑模技术。使用分数李雅普诺夫稳定性表明滑动运动在有限时间内发生。接下来，我们讨论了实现无限接近混沌状态和跟踪误差平衡的控制技术。值得注意的是，可以使用所提出的分数非奇异终端滑模控制技术来控制 FOHDB 和外部随机扰动。最后，通过分析和数值模拟以图形方式说明了所提出的有限时间控制技术的有效性和适用性。