SummaryThis paper deals with the extended design of Mittag‐Leffler state estimator and adaptive synchronization for fractional‐order bidirectional associative memory neural networks with time delays. By the aid of Lyapunov direct approach and Razumikhin‐type method, a suitable fractional‐order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag‐Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag‐Leffler adaptive synchronization by means of some fractional‐order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.