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This article studies synchronization issues for a class of discrete-time fractional-order quaternion-valued uncertain neural networks (DFQUNNs) using nonseparation method. First, based on the theory of discrete-time fractional calculus and quaternion properties, two equalities on the nabla Laplace transform and nabla sum are strictly proved, whereafter three Caputo difference inequalities are rigorously demonstrated. Next, based on our established inequalities and equalities, some simple and verifiable quasi-synchronization criteria are derived under the quaternion-valued nonlinear controller, and complete synchronization is achieved using quaternion-valued adaptive controller. Finally, numerical simulations are presented to substantiate the validity of derived results.