The synchronization issue between fractional-order quaternion-valued neural networks with different structures is more common than that with the same structure in the real world. This paper addresses the Mittag-Leffler stability and adaptive impulsive synchronization between two fractional-order quaternion-valued neural networks with different structures. We also propose two assumptions to analyze the parameters of the nonlinear activation functions. Based on the Mittag-Leffler stability and fractional-order Lyapunov direct method, an impulsive controller scheme is designed to ensure the global stability of fractional-order time-delay quaternion-valued neural networks. We also analyzed the situation when the self-feedback matrix and connection matrix of quaternion-valued fractional-order neural networks with different structures are unknown and designed adaptive impulsive controllers to achieve synchronization. Finally, we verified the feasibility and effectiveness of the proposed theorem through numerical simulation experiments.
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