Global exponential stability of discrete-time almost automorphic Caputo–Fabrizio BAM fuzzy neural networks via exponential Euler technique

Abstract

Exponential Euler discrete schemes have been widely employed in the studies of Caputo fractional order differential equations, but almost no literature concerns the Caputo–Fabrizio case. In current work, exponential discrete form has been set up to study Caputo–Fabrizio fuzzy BAM neural networks(CF-FBAMNNs). The research findings tell someone that (1) the exponential discrete form characterizes the continuous CF-FBAMNNs superior to the classical Euler discrete technique; (2) this type discrete technique pertains to the implicit Euler form, which can be calculated by PECE algorithm. Furthermore, the existence of a unique bounded asymptotically almost automorphic sequence solution and global exponential stability of the proposed discrete-time models are investigated. More importantly, the current works make up for the lacks in the existing literatures and build a set of new theories and methods in studying discrete-time Caputo–Fabrizio models in the fields of science and engineering.