This research demonstrates a focus on the complete synchronization of fractional-order neural networks with bounded parameter uncertainties and information interactions. The drive-response network models considered in this article contain the operators fuzzy AND, fuzzy OR, and nonlinear interaction modes, which makes the systems in this article more generalized. To achieve complete synchronization tasks, we design a new nonlinear adaptive control scheme. Unlike existing control strategies, the controller incorporates a sign function and a monotonically decreasing function, ensuring the boundedness of the controller even as the error approaches zero, while reducing the conservatism of the control intensity. By virtue of fractional calculus properties and inequality analysis techniques, new synchronization criteria of the concerned drive–response networks are established under the adaptive control schemes. Numerical examples demonstrate the effectiveness of the method proposed in this research.