Numerical discretization for the fractional differential equations is applied to the chaotic financial model described by the Caputo derivative. The graphical representations to support the numerical discretization are presented. We profit by analyzing the impact generated by the variations of the saving rate, the per investment cost, and the elasticity of demands in the dynamics of the solutions obtained with our numerical scheme. Notably, we use bifurcation diagrams to quantify the impact of the saving rate, the per investment cost, and the elasticity of demands, as well as the Lyapunov exponent to characterize the existence of chaos for the chosen value of the fractional order. The chaos observed depends strongly on these previously mentioned parameters. We finish by proposing a suitable control to synchronize the drive system and the response fractional financial model, using Lyapunov direct methods. The stability analysis of the equilibrium points of the chaotic financial model has been presented.

中文翻译：

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分数阶导数算子的金融混沌模型分析

分数阶微分方程的数值离散化适用于Caputo导数描述的混沌金融模型。提供了支持数字离散化的图形表示。我们通过分析储蓄率，每项投资成本和需求弹性在数值方案获得的解决方案动态中产生的影响来获利。值得注意的是，我们使用分叉图来量化储蓄率，每投资成本和需求弹性的影响，以及利雅普诺夫指数来表征分数阶所选值的混沌的存在。观察到的混乱很大程度上取决于这些先前提到的参数。通过使用Lyapunov直接方法，提出一个合适的控件来同步驱动系统和响应分数财务模型，以完成本文。提出了混沌金融模型平衡点的稳定性分析。