In this paper, the dynamical behaviors and chaos control of a fractional-order financial system are discussed. The lowest fractional order found from which the system generates chaos is 2.49 for the commensurate order case and 2.13 for the incommensurate order case. Also, period-doubling route to chaos was found in this system. The results of this study were validated by the existence of a positive Lyapunov exponent. Besides, in order to control chaos in this fractional-order financial system with uncertain dynamics, a sliding mode controller is derived. The proposed controller stabilizes the commensurate and incommensurate fractional-order systems. Numerical simulations are carried out to verify the analytical results.

中文翻译：

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分数阶金融系统中的混沌及其滑动模式控制

本文讨论了分数阶金融系统的动力学行为和混沌控制。系统产生混沌的最低分数阶次为 2.49 为 2.49 为 2.49 为 2.13 为非公度阶情况。此外，在该系统中还发现了混沌的周期加倍路径。该研究的结果通过李雅普诺夫正指数的存在得到验证。此外，为了在这个动态不确定的分数阶金融系统中控制混沌，推导了一种滑模控制器。所提出的控制器稳定了相称和不相称的分数阶系统。进行数值模拟以验证分析结果。