The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation
The solutions to fractional differentials equations are very difficult to investigate. In particular, the solutions of fractional partial differential equations are challenging tasks for mathematicians. In the present article, an extension to this idea is presented to obtain the solutions of non-lin...
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Frontiers Media S.A.
2022-07-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2022.924310/full |
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| author | Hassan Khan Hassan Khan Qasim Khan Fairouz Tchier Gurpreet Singh Poom Kumam Poom Kumam Ibrar Ullah Kanokwan Sitthithakerngkiet Ferdous Tawfiq |
| author_facet | Hassan Khan Hassan Khan Qasim Khan Fairouz Tchier Gurpreet Singh Poom Kumam Poom Kumam Ibrar Ullah Kanokwan Sitthithakerngkiet Ferdous Tawfiq |
| author_sort | Hassan Khan |
| collection | DOAJ |
| description | The solutions to fractional differentials equations are very difficult to investigate. In particular, the solutions of fractional partial differential equations are challenging tasks for mathematicians. In the present article, an extension to this idea is presented to obtain the solutions of non-linear fractional Korteweg–de Vries equations. The solutions comparison of the proposed problems is done via two analytical procedures, which are known as the Residual power series method (RPSM) and q-HATM, respectively. The graphical and tabular analysis are presented to show the reliability and competency of the suggested techniques. The comparison has shown the greater contact between exact, RPSM, and q-HATM solutions. The fractional solutions are in good control and provide many important dynamics of the given problems. |
| first_indexed | 2024-12-11T23:48:29Z |
| format | Article |
| id | doaj.art-c5eb5ace9d5d4dbb93017df722fe1497 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-11T23:48:29Z |
| publishDate | 2022-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-c5eb5ace9d5d4dbb93017df722fe14972022-12-22T00:45:33ZengFrontiers Media S.A.Frontiers in Physics2296-424X2022-07-011010.3389/fphy.2022.924310924310The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV EquationHassan Khan0Hassan Khan1Qasim Khan2Fairouz Tchier3Gurpreet Singh4Poom Kumam5Poom Kumam6Ibrar Ullah7Kanokwan Sitthithakerngkiet8Ferdous Tawfiq9Department of Mathematics, Abdul Wali Khan Uniuersity Mardan, Mardan, PakistanDepartment of Mathematics, Near East University, North Nicosia, TurkeyDepartment of Mathematics, Abdul Wali Khan Uniuersity Mardan, Mardan, PakistanDepartment of Mathematics, College of Science, King Saud University, Riyadh, Saudi ArabiaSchool of Mathematical Sciences, Dublin City University, Dublin, IrelandDepartment of Medical Research, China Medical University Hospital, China Medical University, Taichung, TaiwanTheoretical and Computational Science (TaCS) Center, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, ThailandDepartment of Mathematics, Abdul Wali Khan Uniuersity Mardan, Mardan, PakistanIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Bangkok, ThailandDepartment of Mathematics, College of Science, King Saud University, Riyadh, Saudi ArabiaThe solutions to fractional differentials equations are very difficult to investigate. In particular, the solutions of fractional partial differential equations are challenging tasks for mathematicians. In the present article, an extension to this idea is presented to obtain the solutions of non-linear fractional Korteweg–de Vries equations. The solutions comparison of the proposed problems is done via two analytical procedures, which are known as the Residual power series method (RPSM) and q-HATM, respectively. The graphical and tabular analysis are presented to show the reliability and competency of the suggested techniques. The comparison has shown the greater contact between exact, RPSM, and q-HATM solutions. The fractional solutions are in good control and provide many important dynamics of the given problems.https://www.frontiersin.org/articles/10.3389/fphy.2022.924310/fullfractional calculusLaplace transformLaplace residual power series methodfractional partial differential equationpower seriesq-homotopy analysis transform method |
| spellingShingle | Hassan Khan Hassan Khan Qasim Khan Fairouz Tchier Gurpreet Singh Poom Kumam Poom Kumam Ibrar Ullah Kanokwan Sitthithakerngkiet Ferdous Tawfiq The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation Frontiers in Physics fractional calculus Laplace transform Laplace residual power series method fractional partial differential equation power series q-homotopy analysis transform method |
| title | The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation |
| title_full | The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation |
| title_fullStr | The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation |
| title_full_unstemmed | The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation |
| title_short | The Efficient Techniques for Non-Linear Fractional View Analysis of the KdV Equation |
| title_sort | efficient techniques for non linear fractional view analysis of the kdv equation |
| topic | fractional calculus Laplace transform Laplace residual power series method fractional partial differential equation power series q-homotopy analysis transform method |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2022.924310/full |
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