  In this paper, a multi-class Aw-Rascle \textrm{(AR)} model with time
fractional order derivative is presented. The conservative form of the proposed
model is considered for the natural extension and generalization of equations
involved. The fractional order derivative involved in the model equations is
computed by applying the Caputo fractional derivative definition. An explicit
difference scheme is obtained through finite difference method of
discretization. The scheme is shown to be consistent, conditionally stable and
convergent. Numerical flux is computed by original Roe decomposition and an
entropy condition applied to the Roe decomposition. From numerical results, the
effect of fractional-order derivative of time, on the traffic flow of vehicle
classes is determined. Results obtained from the proposed model remain within
limits therefore, they are realistic.
