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

被引:13
作者
Shah, Nehad Ali [1 ,2 ]
Dassios, Ioannis [3 ]
El-Zahar, Essam R. [4 ,5 ]
Chung, Jae Dong [6 ]
Taherifar, Somaye [7 ]
机构
[1] Ton Duc Thang Univ, Informetr Res Grp, Ho Chi Minh City 58307, Vietnam
[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City 58307, Vietnam
[3] Univ Coll Dublin, AMPSAS, Dublin D04, Ireland
[4] Prince Sattam Bin Abdulaziz Univ, Coll Sci & Humanities Al Kharj, Dept Math, POB 83, Al Kharj 11942, Saudi Arabia
[5] Menoufia Univ, Fac Engn, Dept Basic Engn Sci, Shibin Al Kawm 32511, Egypt
[6] Sejong Univ, Dept Mech Engn, Seoul 05006, South Korea
[7] Shahid Chamran Univ Ahvaz, Fac Math & Comp Sci, Dept Comp Sci, Ahvaz 61355145, Iran
关键词
Fractional Fornberg– Whitham equation; variational iteration transform method; Shehu decomposition method; partial differential equation; approximate solution; Caputo’ s operator; CONSERVATION-LAWS; SHEHU TRANSFORM; DIFFERENTIAL-EQUATIONS;
D O I
10.3390/math9020141
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:1 / 14
页数:14
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