<p>In order to better capture the dynamic characteristics of human-driving vehicles, numerous scholars have proposed various car-following models. Full velocity difference model (FVD) is a famous car-following model in the traffic flow theory to illustrate the traffic phenomenon among them. In particular, fractional calculus can precisely depict and predict various complex phenomena with the memory effect and nonlinear characteristics. Thus, this paper creatively proposes a fractional-order full velocity difference model (FFVD). Next, we consider the stochasticity and time-delay of driving behavior, which is the random value at different time. Then, we incorporate the average velocity and position of the leading vehicle during time delay processes as state variables in our model. In addition, we propose an improved whale optimization algorithm, named as WOADRL, fused with dynamic reverse mutual learning and Lévy flight strategy for calibrating the parameters of fractional-order car-following models more precisely and stably. Furthermore, the proposed car-following model is compared with other exsiting models on three data sets separately. The results indicate that the new model can reproduce real driving behavior more accurately. Finally, we also find that the fractional car-following model has stronger stability and modelling effect under different disturbances, which is tested in two driving scenarios.</p>