The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method
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 tran...
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| Format: | Article |
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MDPI AG
2021-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/2/141 |
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| author | Nehad Ali Shah Ioannis Dassios Essam R. El-Zahar Jae Dong Chung Somaye Taherifar |
| author_facet | Nehad Ali Shah Ioannis Dassios Essam R. El-Zahar Jae Dong Chung Somaye Taherifar |
| author_sort | Nehad Ali Shah |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T05:17:28Z |
| format | Article |
| id | doaj.art-bc13f47b43214a13ba95faabea5ef24e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:17:28Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bc13f47b43214a13ba95faabea5ef24e2023-12-03T12:44:30ZengMDPI AGMathematics2227-73902021-01-019214110.3390/math9020141The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform MethodNehad Ali Shah0Ioannis Dassios1Essam R. El-Zahar2Jae Dong Chung3Somaye Taherifar4Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 58307, VietnamAMPSAS, University College Dublin, D04 Dublin, IrelandDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi ArabiaDepartment of Mechanical Engineering, Sejong University, Seoul 05006, KoreaDepartment of Computer Sciences, Faculty of Mathematics and Computer Sciences, Shahid Chamran University of Ahvaz, Ahvaz 61355-145, IranIn 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.https://www.mdpi.com/2227-7390/9/2/141Fractional Fornberg–Whitham equationvariational iteration transform methodShehu decomposition methodpartial differential equationapproximate solutionCaputo’s operator |
| spellingShingle | Nehad Ali Shah Ioannis Dassios Essam R. El-Zahar Jae Dong Chung Somaye Taherifar The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method Mathematics Fractional Fornberg–Whitham equation variational iteration transform method Shehu decomposition method partial differential equation approximate solution Caputo’s operator |
| title | The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method |
| title_full | The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method |
| title_fullStr | The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method |
| title_full_unstemmed | The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method |
| title_short | The Variational Iteration Transform Method for Solving the Time-Fractional Fornberg–Whitham Equation and Comparison with Decomposition Transform Method |
| title_sort | variational iteration transform method for solving the time fractional fornberg whitham equation and comparison with decomposition transform method |
| topic | Fractional Fornberg–Whitham equation variational iteration transform method Shehu decomposition method partial differential equation approximate solution Caputo’s operator |
| url | https://www.mdpi.com/2227-7390/9/2/141 |
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