<p>In this paper, the quasi-synchronization and adaptive synchronization are explored for fully complex-valued uncertain fractional-order competitive neural networks (FCUFCNNs) based on nonlinear control method. First of all, some novel lemmas containing the inequalities of complex variable and fractional differential equation are proposed to bring new ideas for analyzing the dynamics of complex-valued systems. Secondly, two new nonlinear controllers are designed, and some sufficient criteria are obtained to achieve the quasi-synchronization and adaptive synchronization of FCUFCNNs by means of proposed lemmas as well as designed controllers. In the end, two numerical examples are given to check the effectiveness of derived synchronization results of FCUFCNNs, and moreover its application in image encryption is substantiated.</p>