Exponential Euler scheme of multi-delay Caputo–Fabrizio fractional-order differential equations

Abstract

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.