In this paper, we discussed the fixed-time synchronization of fractional-order memristorbased fuzzy cellular neural networks (FMFCNNs) with time-varying delays. Based on the differential inclusion theory and discontinuous state feedback control technique, some useful novel criteria of the fixedtime synchronization for FMFCNNs are derived by constructing appropriate Lyapunov function. The results in our paper improve and generalize current literature research results significantly. Finally, the effectiveness of our control schemes for the fixed-time synchronization is demonstrated through numerical simulations. INDEX TERMS Fractional-order memristor-based fuzzy cellular neural networks, fixed-time synchronization, state feedback control technique, Lyapunov direct method.