Fractional analysis provides useful tools to describe natural phenomena, and therefore, it is more convenient to describe models of satellites. This work illustrates rich chaotic behaviors that exist in a fractional-order model for satellite with and without time-delay. The proof for existence and uniqueness of the satellite model’s solution with and without time-delay is shown. Chaos control is achieved in this system via a simple linear feedback control criterion. Chaotic attractors and chaos control are also found in a time-delay version of the proposed fractional-order satellite system. Various tools based on numerical simulations such as 2D and 3D attractors and bifurcation diagrams are used to illustrate the variety of rich chaotic dynamics in the satellite models.

中文翻译：

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分数阶卫星模型及其时延模型中的混沌动力学和混沌控制

分数分析为描述自然现象提供了有用的工具，因此更方便地描述卫星模型。这项工作说明了存在于具有和不具有时滞的卫星的分数阶模型中的丰富混沌行为。显示了卫星模型解的存在性和唯一性的证明，有和没有时滞。该系统通过简单的线性反馈控制准则实现混沌控制。在提出的分数阶卫星系统的延时版本中也发现了混沌吸引子和混沌控制。基于数值模拟的各种工具，如 2D 和 3D 吸引子和分叉图，用于说明卫星模型中各种丰富的混沌动力学。