New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method
Symmetry performs an essential function in finding the correct techniques for solutions to time space fractional differential equations (TSFDEs). In this article, we present the Novel Analytic Method (NAM) for approximate solutions of the linear and non-linear KdV equation for TSFDs. To enunciate th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/12/2296 |
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| author | Mariam Sultana Uroosa Arshad Md. Nur Alam Omar Bazighifan Sameh Askar Jan Awrejcewicz |
| author_facet | Mariam Sultana Uroosa Arshad Md. Nur Alam Omar Bazighifan Sameh Askar Jan Awrejcewicz |
| author_sort | Mariam Sultana |
| collection | DOAJ |
| description | Symmetry performs an essential function in finding the correct techniques for solutions to time space fractional differential equations (TSFDEs). In this article, we present the Novel Analytic Method (NAM) for approximate solutions of the linear and non-linear KdV equation for TSFDs. To enunciate the non-integer derivative for the aforementioned equation, the Caputo operator is manipulated. Furthermore, the formula implemented is a numerical way that is postulated from Taylor’s series, which confirms an analytical answer in the form of a convergent series. For delineation of the efficiency and functionality of the method in question, four applications are exemplified along with graphical interpretation and numerical solutions to finitely illustrate the behavior of the solution to this equation. Moreover, the 3D graphs of some of these numerical examples are plotted with specific values. Observing the effectiveness of this process, we can easily decide that this process can be implemented to other TSFDEs applied in the mathematical modeling of a real-world aspect. |
| first_indexed | 2024-03-10T03:01:05Z |
| format | Article |
| id | doaj.art-c1b6e7516eff4806be743396255ddff6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T03:01:05Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c1b6e7516eff4806be743396255ddff62023-11-23T10:45:04ZengMDPI AGSymmetry2073-89942021-12-011312229610.3390/sym13122296New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic MethodMariam Sultana0Uroosa Arshad1Md. Nur Alam2Omar Bazighifan3Sameh Askar4Jan Awrejcewicz5Department of Mathematics, Federal Urdu University of Arts, Sciences & Technology, Karachi 75300, PakistanDepartment of Mathematics, Federal Urdu University of Arts, Sciences & Technology, Karachi 75300, PakistanDepartment of Mathematics, Pabna University of Science & Technology, Pabna 6600, BangladeshSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, ItalyDepartment of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, PolandSymmetry performs an essential function in finding the correct techniques for solutions to time space fractional differential equations (TSFDEs). In this article, we present the Novel Analytic Method (NAM) for approximate solutions of the linear and non-linear KdV equation for TSFDs. To enunciate the non-integer derivative for the aforementioned equation, the Caputo operator is manipulated. Furthermore, the formula implemented is a numerical way that is postulated from Taylor’s series, which confirms an analytical answer in the form of a convergent series. For delineation of the efficiency and functionality of the method in question, four applications are exemplified along with graphical interpretation and numerical solutions to finitely illustrate the behavior of the solution to this equation. Moreover, the 3D graphs of some of these numerical examples are plotted with specific values. Observing the effectiveness of this process, we can easily decide that this process can be implemented to other TSFDEs applied in the mathematical modeling of a real-world aspect.https://www.mdpi.com/2073-8994/13/12/2296Novel Analytic Method (NAM)Taylor’s seriesKdV equation for time-space fractional derivatives |
| spellingShingle | Mariam Sultana Uroosa Arshad Md. Nur Alam Omar Bazighifan Sameh Askar Jan Awrejcewicz New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method Symmetry Novel Analytic Method (NAM) Taylor’s series KdV equation for time-space fractional derivatives |
| title | New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method |
| title_full | New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method |
| title_fullStr | New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method |
| title_full_unstemmed | New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method |
| title_short | New Results of the Time-Space Fractional Derivatives of Kortewege-De Vries Equations via Novel Analytic Method |
| title_sort | new results of the time space fractional derivatives of kortewege de vries equations via novel analytic method |
| topic | Novel Analytic Method (NAM) Taylor’s series KdV equation for time-space fractional derivatives |
| url | https://www.mdpi.com/2073-8994/13/12/2296 |
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