Analytical method to solve the local fractional vehicular traffic flow model. (16th December 2021)

• Record Type: Journal Article
• Authors: Singh, Nisha; Kumar, Kranti; Goswami, Pranay; Jafari, Hossein
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 7(2022)
• Page Start: 3983
• Page End: 4001
• Publication Date: 2021-12-16
• Subjects: local fractional calculus -- local variational iteration method -- LWR model -- mathematical modeling -- traffic flow; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8027
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper presents a new method to solve the local fractional partial differential equations (LFPDEs) describing fractal vehicular traffic flow. Firstly, the existence and uniqueness of solutions to LFPDEs were proved and then two schemes known as the basic method (BM) and modified local fractional variational iteration method (LFVIM) were developed to solve the local fractional PDEs. Multiple studies have been reported in the literature to solve these problems using iterative methods which are time‐consuming and prone to errors. For linear problems, basic method was found highly accurate and computationally sound. We derived a modified version of LFVIM to investigate and obtain the nondifferentiable solutions of linear, nonlinear, and nonhomogeneous LFPDEs arising in fractal vehicular traffic flow through illustrative examples. Study results show that both schemes are very effective and can be used successfully to solve fractal vehicular traffic flow problems.