Adaptive quaternion projective synchronization of fractional order delayed neural networks in quaternion field

•By combining the advantages of fractional calculus and quaternion valued neural network, and considering the factors of time-delay, the model of fractional order quaternion valued neural network with time delay is established, which is further extended in the research domains of neural networks.•A new fractional order quaternion self conjugate inequality is constructed, which plays a key role in achieving the results.•Finally, compared with real projective synchronization, quaternion projective synchronization of FODQVNN is discussed in this paper, which is more general and complex. This paper focuses on investigating quaternion projective synchronization of the fractional order delayed quaternion valued neural networks(FODQVNN). By applying Lyapunov direct method rather than decomposition method, quaternion projective synchronization of FODQVNN is discussed, in which the projective coefficient is set to quaternion number. Through designing appropriate adaptive controllers, some succinct criteria ascertaining the quaternion projective synchronization issues for considering systems are obtained. Finally, an example is presented to test the effectiveness of the theoretical scheme.