Identifying the parameters of the chaos phenomena in the economic-financial systems is a critical issue to control and avoid the financial crises and bogging the market down. Therefore, in this paper, an efficient and reliable optimization algorithm is developed to identify the corresponding parameters of that chaotic dynamical behavior in the fractional-order chaotic, chaotic with noise, and hyper-chaotic financial systems. The introduced algorithm is a cooperation among the fractional calculus (FC) perspective and the basic cuckoo search algorithm to enhance the stochastic cuckoo’s walk via considering the cuckoo’s earlier behaviors from memory. The developed fractional-order cuckoo search (FO-CS) is validated with twenty-eight functions of CEC2017 with different dimensions. Several measures and non-parametric statistical tests are presented to demonstrate the superiority of the introduced algorithm while compared with the CS and the state-of-the-art techniques. The results show that merging of FC properties magnifies CS’s efficiency, convergence speed, and robustness against the complexity of the considered CEC benchmarks suite and the non-linearity of the fractional-order chaotic, chaotic with noise, and hyper-chaotic financial systems.

确定经济金融体系中混乱现象的参数是控制和避免金融危机并使市场陷入困境的关键问题。因此，在本文中，开发了一种有效且可靠的优化算法，以识别分数阶混沌，带噪声混沌和超混沌金融系统中该混沌动力学行为的相应参数。引入的算法是分数微积分（FC）透视图和基本的布谷鸟搜索算法之间的合作，可通过考虑内存中的布谷鸟的早期行为来增强随机的布谷鸟走动。所开发的分数杜鹃搜索（FO-CS）已通过具有不同尺寸的CEC2017的28个功能进行了验证。提出了几种措施和非参数统计测试，以证明引入的算法与CS和最新技术相比的优越性。结果表明，FC属性的合并会放大CS的效率，收敛速度和鲁棒性，以应对考虑的CEC基准套件的复杂性以及分数阶混沌，带噪声的混沌和超混沌金融系统的非线性。