The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method

Nehad Ali Shah, Ioannis Dassios, Essam R. El-Zahar, Jae Dong Chung and Somaye Taherifar
Additional contact information
Nehad Ali Shah: Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 58307, Vietnam
Ioannis Dassios: AMPSAS, University College Dublin, D04 Dublin, Ireland
Essam R. El-Zahar: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Somaye Taherifar: Department of Computer Sciences, Faculty of Mathematics and Computer Sciences, Shahid Chamran University of Ahvaz, Ahvaz 61355-145, Iran

Mathematics, 2021, vol. 9, issue 2, 1-14

Abstract: In this article, modified techniques, namely the variational iteration transform and Shehu decomposition method, are implemented to achieve an approximate analytical solution for the time-fractional Fornberg–Whitham equation. A comparison is made between the results of the variational iteration transform method and the Shehu decomposition method. The solution procedure reveals that the variational iteration transform method and Shehu decomposition method is effective, reliable and straightforward. The variational iteration transform methods solve non-linear problems without using Adomian’s polynomials and He’s polynomials, which is a clear advantage over the decomposition technique. The solutions achieved are compared with the corresponding exact result to show the efficiency and accuracy of the existing methods in solving a wide variety of linear and non-linear problems arising in various science areas.

Keywords: Fractional Fornberg–Whitham equation; variational iteration transform method; Shehu decomposition method; partial differential equation; approximate solution; Caputo’s operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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