Analytical solution of local fractal continuum traffic flow model

This study developed a continuum traffic flow model with local fractional derivatives. This model overcomes the non-differentiable traffic parameters arising in vehicular traffic flow. The proposed model is solved using the local fractional Laplace variational iteration method (LFLVIM) and is well suited for analyzing the dynamical evolution of non-differentiable traffic density and speed function. Furthermore, the stability of the solution for the continuum model has also been discussed. Illustrative examples are also discussed to show the effectiveness of employing LFLVIM in the suggested model. Additionally, numerical simulations for each instance have been displayed. This research indicates that the utilized iterative approach is efficient and may be used to derive the non-differentiable solution to the proposed continuum traffic model.