Estimate scheme for fractional order-dependent fixed-time synchronization on Caputo quaternion-valued BAM network systems with time-varying delays

In this paper, an estimate scheme for derivative order-dependent fixed-time synchronization (F-TS) on Caputo quaternion-valued BAM neural networks (QVBAMNNs) with time-varying delays is implemented. A novel fractional-order (FO) F-T stability lemma is established by the synthetic properties of fractional calculus. The appropriate feedback controllers are designed to realize the F-TS between the master-slave systems. Based on the Lyapunov functional method and multiple inequality techniques, the F-TS criterion of FOQVBAMNNs is obtained. Furthermore, the upper bound of settling time is predicted and controlled by the Caputo derivative order and system parameters, which is independent of the initial state. Finally, two simulation examples manifest the feasibility and validity of the results on F-TS and the control strategies.