α-stability and α-synchronization for fractional-order neural networks.

In this paper, a class of fractional-order neural networks is investigated. First, α-exponential stability is introduced as a new type of stability and some effective criteria are derived for such kind of stability of the addressed networks by handling a new fractional-order differential inequality. Based on the results, the existence and α-exponential stability of the equilibrium point are considered. Besides, the synchronization of fractional chaotic networks is also proposed. Finally, several examples with numerical simulations are given to show the effectiveness of the obtained results.