This research focuses on controlling fixed-time synchronization (FixTS) in a time-delayed fuzzy memristor-based neural network (TDFMNN). To achieve FixTS and improve convergence speed, a discontinuous state feedback controller (StFC) incorporating a unique exponential function is developed for the memristor-based neural network (MNN) drive-response system (DRS). The FixTS is analyzed using the indefinite derivative Lyapunov function approach. The proposed TDFMNN incorporates multiple factors, such as memristor, time-variation of coefficients, time-delay, and fuzzy elements, making the model more practical compared to existing studies. The StFC is designed using the fixed-time stability (FixS) theory of the exponential function, which requires few parameters, thereby simplifying controller design and implementation. Numerical simulations are conducted to evaluate the performance of the proposed control strategy on two-dimensional and three-dimensional TDMNNs.