This paper establishes the basic structure of the exponential Euler difference form for Caputo–Fabrizio fractional-order differential equations (CF-FODEs) with multiple lags. The research shows that the acquired difference form (i.e., discrete-time CF-FODEs) belongs to the scope of implicit Euler differences and then the fractional PECE algorithm is proposed to solve this implicit difference. At last, global dynamics of the discrete-time CF-FODEs is discussed from the viewpoint of control theory.

中文翻译：

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多延迟 Caputo-Fabrizio 分数阶微分方程的指数欧拉格式

本文建立了 具有多重滞后的Caputo-Fabrizio 分数阶微分方程(CF-FODE)的指数欧拉差分形式的基本结构。研究表明，获得的差分形式 （即离散时间CF-FODEs）属于隐式欧拉差分的范围，于是提出了分数PECE算法来解决这种隐式差分。最后，从控制理论的角度讨论了离散时间CF-FODEs的全局动力学。