<p>There are various neurons in the brain’s neural network, and the study of heterogeneous neural networks is more relevant to actual biological neural networks. Fractional-order differentiation provides a better description of objects in the natural world than integer-order differentiation. In this paper, a heterogeneous fractional-order Hopfield neural network system with four neurons is constructed by coupling two small Hopfield neural networks with different neurons using a memristor. The neurons of the two Hopfield subnetworks have different activation functions, simulating neural network modules with heterogeneous functions in diverse regions of the brain. The designed fractional-order system is calculated using the predictor-corrector Adams–Bashforth–Moulton (ABM) method and the potential dynamical behavior of the system is explored in detail using numerical analyses such as bifurcation diagrams, spectral entropy complexity, and time domain diagrams. It is found that the neural network system produces attractors with different shapes as the memristor coupling strength and fractional order are varied. Moreover, the neurons in the neural network have spiking firing patterns. In addition, the numerical analysis results demonstrate rich and complex dynamical behaviors such as coexisting attractors. Based on the Grunwald-Letnikov (G-L) definition, we design a FPGA implementation for the proposed fractional-order memristive Hopfield neural network.</p>