A generalized local fractional LWR model of vehicular traffic flow and its solution

Abstract

In this study, a generalized nonlinear local fractional Lighthill‐Whitham‐Richards (LFLWR) model has been developed. The local fractional variational iteration method (LFVIM) solves and analyzes the proposed model. Numerous works have been described in the past to address linear LWR and linear LFLWR models. This research highlighted on generalized nonlinear LFLWR model, and LFVIM is employed to derive non‐differentiable solutions of the suggested model. The existence and uniqueness of the solution of LFLWR model have also been established. Furthermore, several exemplary instances are discussed to demonstrate the success of implementing LFVIM to the proposed model. The numerical simulations for each of the cases have also been shown. Additionally, the obtained solutions of the suggested model have been compared with the solutions of the classical LWR model with non‐differentiable conditions in few examples. The study demonstrates that the employed iterative scheme is quite efficient and can be utilized to obtain the non‐differentiable solution to the proposed generalized nonlinear LFLWR traffic flow model.