In this study, we introduce two distinct stability criteria, namely finite-time stability (FTS) and finite-time contractive stability (FTCS), specifically designed for fractional-order coupled neural networks (FOCNNs). The key to achieving these stability criteria lies in the effective application of impulsive adaptive control (IAC). Notably, the adaptive generator intermittently changes at specific impulsive instants. For this purpose, we initially propose some sufficient conditions for fractional-domain and Lyapunov theory. The construction of the Lyapunov function assumes a crucial role in analyzing the stability criteria. Furthermore, comprehensive convergence analyses are provided to support by impulsive adaptive feedback protocols. This innovative approach ensures a continuous maintenance of stability performance in the FOCNNs. Subsequently, we validate our theoretical findings through numerical simulations, solidifying the practicality and performance of our proposed method.