In this paper we investigate controller design problem for finite-time and fixed-time stabilization of fractional-order memristive complex-valued BAM neural networks (FMCVBAMNNs) with uncertain parameters and time-varying delays. By using the Lyapunov theory, differential inclusion theory, and fractional calculus theory, finite-time stabilization condition for fractional-order memristive complex-valued BAM neural networks and the upper bound of the settling time for stabilization are obtained. The nonlinear complex-valued activation functions are split into two (real and imaginary) components. Moreover, the settling time of fixed time stabilization, that does not depend upon the initial values, is merely calculated. A novel criterion for guaranteeing the fixed-time stabilization of FMCVBAMNNs is derived. Our control scheme achieves system stabilization within bounded time and has an advantage in convergence rate. Numerical simulations are furnished to demonstrate the effectiveness of the theoretical analysis. (C) 2020 Elsevier Ltd. All rights reserved.