This article concentrates on the finite-time synchronization (FTS) for multi-weighted fractional-order coupled neural networks (MFCNNs) with fixed and adaptive couplings. A new dynamic model, which involves coupled neural networks with fractional order and multi-weighted couplings, is proposed. Furthermore, an adaptive law to adjust the coupling weights is devised to ensure the FTS of such a complex model. First, by using fractional-order calculus properties and inequality techniques, a finite-time fractional differential inequality is presented, which considerably extends the prior result. Second, by the Lyapunov stability theory and the fractional-order inequality, several sufficient conditions are acquired to make sure the FTS for MFCNNs. Moreover, the influence of the system's order on the FTS is also uncovered. Finally, a numerical simulation example and a practical simulation example are provided to demonstrate the validity of the obtained criteria.

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