Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow

Yang Li,Sheng-Da Zeng,Yang Zhao,Long-Fei Wang

doi:10.1155/2014/649318

Abstract

We discuss the line partial differential equations arising in fractal vehicular traffic flow. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. The obtained results show the efficiency and accuracy of implements of the present method.

Highlights

Fractional differential equations with arbitrary orders were applied to model the real-world problems for science and engineering
The initial and boundary conditions for line partial differential equations arising in fractal vehicular traffic flow read as follows: φ (x, 0) = Eα, (25)
The initial and boundary conditions for line partial differential equations arising in fractal vehicular traffic flow with the parameter μ = 1 are φ (x, 0) = sinhα, (35)

Summary

Introduction

Fractional differential equations with arbitrary orders were applied to model the real-world problems for science and engineering. Many researchers present their applications with solid mechanics, heat transfer, fluid mechanics, transport process, water motion, and quantum mechanics. The linear differential equation arising in fractal vehicular traffic flow was suggested in [31]. We use the local fractional Laplace variational iteration method to solve the linear differential equation arising in fractal vehicular traffic flow.

The Lighthill-Whitham-Richards Model on a Finite Length Highway

Local Fractional Laplace Variational Iteration Method

Conclusions