In this article, we present the basic concepts of fractional calculus and control and synchronization of fractional‐order chaotic satellite system . Existence and uniqueness solutions of fractional‐order satellite system are discussed and local stability of the system at the equilibrium points are studied. The lowest dimension of chaotic attractor of satellite system is 2.88 which is obtained through utilization of the fractional dynamics and computational simulation. Lyapunov exponents and bifurcation diagrams are drawn to measure the existence of chaos in the system. Feedback control method for chaos control in the fractional‐order satellite system is achieved. Synchronization of two identical noninteger order chaotic satellite systems are achieved through adaptive control methodology.

中文翻译：

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使用反馈和自适应控制技术的分数阶混沌卫星系统的控制和同步

在本文中，我们介绍了分数演算以及分数阶混沌卫星系统的控制和同步的基本概念。讨论了分数阶卫星系统的存在性和唯一性解，并研究了该系统在平衡点处的局部稳定性。卫星系统混沌吸引子的最小维数为2.88，这是通过利用分数动力学和计算仿真获得的。绘制李雅普诺夫指数和分叉图以测量系统中混沌的存在。实现了分数阶卫星系统混沌控制的反馈控制方法。通过自适应控制方法可以实现两个相同的非整数阶混沌卫星系统的同步。