<p>In this paper, we consider the dynamics of Caputo fractional order predator–prey models with Allee effect in prey and refuge in proportion to the two species. We first investigate the model without delay including the well-posedness, the existence of non-negative equilibrium, and the global stability for all non-negative equilibria, and the fractional order Hopf bifurcation of the coexistence equilibrium, which indicates that the combination effect of Allee effect and prey refuge on system dynamics. Then, for the delayed model, we show that the coexistence equilibrium is locally asymptotically stable for any delay under certain conditions. Finally, numerical simulation is given to display the validity of the main results, and it also reveals the differences in dynamics between integer order and fractional order systems.</p>