Abstract It is well known that the transmission of nerve signals is closely related to the incidence and production of vascular diseases. However, due to the multilayered and complex structure of the vascular wall, although a series of studies have been carried out, the mechanism of vascular diseases is difficult to fully understand. In this paper, the fractional constitutive equation is used to study numerically the transmission of nerve signals in the vascular wall. On the basis of considering the effect of substance transport in the vascular layer, a new comprehensive model was established to describe and analyze the voltage trajectory of neuron activity using multi-time-scale dynamics induced by correlated membranes combined with non-Markov processes. The results show that our fractional order model can better describe the process of neurotransmission. By changing the fractional order, we can show in vitro the up-and-down spike adaptation found in the experiments of neocortical pyramidal cells and parietal neurons.