MITTAG-LEFFLER STABILITY ANALYSIS OF TEMPERED FRACTIONAL NEURAL NETWORKS WITH SHORT MEMORY AND VARIABLE-ORDER

A class of tempered fractional neural networks is proposed in this paper. Stability conditions for tempered fractional neural networks are provided by using Banach fixed point theorem. Attractivity and Mittag-Leffler stability are given. In order to show the efficiency and convenience of the method used, tempered fractional neural networks with and without delay are discussed, respectively. Furthermore, short memory and variable-order tempered fractional neural networks are proposed under the global conditions. Finally, two numerical examples are used to demonstrate the theoretical results.

Automated summary

This paper proposes a class of tempered fractional neural networks and provides stability conditions using the Banach fixed point theorem, along with attractiveness and Mittag-Leffler stability. The efficiency and convenience of the method are demonstrated through discussions on tempered fractional neural networks with and without delay. Additionally, short memory and variable-order tempered fractional neural networks are proposed under global conditions, with theoretical results demonstrated through numerical examples.