Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences
In this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation, which model the creation of nonlinear water waves in the long wavelength area and the transmission of signals. We implemented two novel techniques, namely the homotopy perturbation...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/8/584 |
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| author | Mashael M. AlBaidani Abdul Hamid Ganie Fahad Aljuaydi Adnan Khan |
| author_facet | Mashael M. AlBaidani Abdul Hamid Ganie Fahad Aljuaydi Adnan Khan |
| author_sort | Mashael M. AlBaidani |
| collection | DOAJ |
| description | In this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation, which model the creation of nonlinear water waves in the long wavelength area and the transmission of signals. We implemented two novel techniques, namely the homotopy perturbation transform method and the Elzaki transform decomposition method. The derivative having fractional-order is taken in Caputo sense. The Adomian and He’s polynomials make it simple to handle the nonlinear terms. To illustrate the adaptability and effectiveness of derivatives with fractional order to represent the water waves in long wavelength regions, numerical data have been given graphically. A key component of the Kawahara equation is the symmetry pattern, and the symmetrical nature of the solution may be observed in the graphs. The importance of our suggested methods is illustrated by the convergence of analytical solutions to the precise solutions. The techniques currently in use are straightforward and effective for solving fractional-order issues. The offered methods reduced computational time is their main advantage. It will be possible to solve fractional partial differential equations using the study’s findings as a tool. |
| first_indexed | 2024-03-10T23:55:48Z |
| format | Article |
| id | doaj.art-e55a53ca3fe444cc967de27f6fc607ce |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T23:55:48Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e55a53ca3fe444cc967de27f6fc607ce2023-11-19T01:10:59ZengMDPI AGFractal and Fractional2504-31102023-07-017858410.3390/fractalfract7080584Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied SciencesMashael M. AlBaidani0Abdul Hamid Ganie1Fahad Aljuaydi2Adnan Khan3Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj 11942, Saudi ArabiaBasic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi ArabiaDepartment of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj 11942, Saudi ArabiaDepartment of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, PakistanIn this paper, we examined the approximations to the time-fractional Kawahara equation and modified Kawahara equation, which model the creation of nonlinear water waves in the long wavelength area and the transmission of signals. We implemented two novel techniques, namely the homotopy perturbation transform method and the Elzaki transform decomposition method. The derivative having fractional-order is taken in Caputo sense. The Adomian and He’s polynomials make it simple to handle the nonlinear terms. To illustrate the adaptability and effectiveness of derivatives with fractional order to represent the water waves in long wavelength regions, numerical data have been given graphically. A key component of the Kawahara equation is the symmetry pattern, and the symmetrical nature of the solution may be observed in the graphs. The importance of our suggested methods is illustrated by the convergence of analytical solutions to the precise solutions. The techniques currently in use are straightforward and effective for solving fractional-order issues. The offered methods reduced computational time is their main advantage. It will be possible to solve fractional partial differential equations using the study’s findings as a tool.https://www.mdpi.com/2504-3110/7/8/584Elzaki transformKawahara and modified Kawahara equationshomotopy perturbation methodAdomian decomposition methodCaputo operator |
| spellingShingle | Mashael M. AlBaidani Abdul Hamid Ganie Fahad Aljuaydi Adnan Khan Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences Fractal and Fractional Elzaki transform Kawahara and modified Kawahara equations homotopy perturbation method Adomian decomposition method Caputo operator |
| title | Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences |
| title_full | Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences |
| title_fullStr | Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences |
| title_full_unstemmed | Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences |
| title_short | Application of Analytical Techniques for Solving Fractional Physical Models Arising in Applied Sciences |
| title_sort | application of analytical techniques for solving fractional physical models arising in applied sciences |
| topic | Elzaki transform Kawahara and modified Kawahara equations homotopy perturbation method Adomian decomposition method Caputo operator |
| url | https://www.mdpi.com/2504-3110/7/8/584 |
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