In this paper, we developed the fractional-order finance system transmission model. The main objective of this paper is to construct and evaluate a fractional derivative to track the shape of the dynamic chaotic financial system of fractional order. The numerical solution for fractional-order financial system is determined using the Atangana–Baleanu–Caputo (ABC) and Caputo derivatives. Picard–Lindelof’s method shows the existence and uniqueness of the solution. Numerical techniques show that ABC derivative strategy can be used effectively to overcome the risk of investment. An active control strategy for controlling chaos is used in this system. The stabilisation of equilibrium is obtained by both theoretical analysis and simulation results.

中文翻译：

---

分数阶金融系统的动力学行为

在本文中，我们开发了分数阶金融系统传输模型。本文的主要目标是构建和评估分数阶导数，以跟踪分数阶动态混沌金融系统的形状。分数阶金融系统的数值解是使用 Atangana-Baleanu-Caputo (ABC) 和 Caputo 导数确定的。Picard–Lindelof 的方法显示了解的存在性和唯一性。数值技术表明，ABC衍生策略可以有效地克服投资风险。该系统采用了一种控制混沌的主动控制策略。平衡的稳定是通过理论分析和模拟结果获得的。