New inequalities to finite-time synchronization analysis of delayed fractional-order quaternion-valued neural networks

In order to overcome the complexity of the theoretical analysis caused by using decomposition method to explore the finite-time synchronization behavior of fractional-order quaternion-valued neural networks (FOQVNNs), we aim to deal with this problem directly instead of decomposition. Firstly, two inequalities about quaternion are developed to broaden the current achievements in quaternion field. Secondly, a fractional differential inequality is established by using Laplace transform and applying the definition of Mittag-Leffler function. Then, by employing the presented inequalities and two different quaternion control strategies, some new conditions are derived to guarantee the finite-time synchronization of the delayed FOQVNNs. Finally, two numerical examples are given to illustrate the correctness of the main results.