Projective synchronization of fractional-order quaternion-valued neural networks with Mittag-Leffler kernel

We consider fractional-order quaternion-valued neural networks (FO-QVNNs) with Mittag-Leffler kernel and study projective synchronization. We establish Mittag-Leffler projective synchronization (MLPS) and asymptotic projective synchronization for the FO-QVNNs. Initially, a novel fractional differential inequality for the fractional derivative is established to study the synchronization of fractional-order systems. Subsequently, quaternion-valued feedback controllers are designed. Conditions for MLPS are then formulated using quaternion techniques, the proposed inequality and the properties of fractional calculus. The effectiveness and practicality of the proposed methodologies are displayed through numerical simulations in a concrete case.