Computational Analysis of Local Fractional LWR Model Occurring in a Fractal Vehicular Traffic Flow

Abstract

In this paper, we implement computational methods, namely the local fractional natural homotopy analysis method (LFNHAM) and local fractional natural decomposition method (LFNDM), to examine the solution for the local fractional Lighthill–Whitham–Richards (LFLWR) model occurring in a fractal vehicular traffic flow. The LWR approach preferably models the traffic flow and represents the traffic patterns via the supposition of speed–density equilibrium relationship and continuity equation. This model is mostly preferred for modeling of traffic flow because of its simple approach and interpretive ability to examine the qualitative patterns of traffic flow. The methods applied here incorporate the local fractional natural transform (LFNT) and derive the solutions for the LFLWR model in a closed form. Two examples are provided to demonstrate the accuracy and efficiency of the suggested methods. Furthermore, the numerical simulations have also been presented for each of the examples in the fractal domain. Additionally, the explored solutions for both examples have also been compared and are in good match with already existing solutions in literature. The methods applied in this work make the computational process easier as compared to other iterative methods and still provide precise solutions.

Keywords

• local fractional Lighthill–Whitham–Richards model
• fractal vehicular traffic flow
• local fractional natural homotopy analysis method
• local fractional natural decomposition method
• local fractional natural transform