Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive Media
The aim of this paper is to investigate the approximate solutions of nonlinear temporal fractional models of Gardner and Cahn-Hilliard equations. The fractional models of the Gardner and Cahn-Hilliard equations play an important role in pulse propagation in dispersive media. The time-fractional deri...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/4422186 |
| _version_ | 1811181732237410304 |
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| author | Mohammed Al-Smadi Shrideh Al-Omari Yeliz Karaca Shaher Momani |
| author_facet | Mohammed Al-Smadi Shrideh Al-Omari Yeliz Karaca Shaher Momani |
| author_sort | Mohammed Al-Smadi |
| collection | DOAJ |
| description | The aim of this paper is to investigate the approximate solutions of nonlinear temporal fractional models of Gardner and Cahn-Hilliard equations. The fractional models of the Gardner and Cahn-Hilliard equations play an important role in pulse propagation in dispersive media. The time-fractional derivative is observed in the conformable framework. In this orientation, a reliable computationally algorithm is designed and developed by following a residual error and multivariable power series expansion. Basically, the approximate solutions of pulse wave function of the fractional higher-order Gardner and Cahn-Hilliard equations are obtained in the form of a conformable convergent fractional series. Relevant consequences are theoretically and numerically investigated under the conformable sense. Besides, the analysis of the error and convergence of the developed technique are discussed. Some of the unidirectional homogeneous physical applications of the posed models in a finite compact regime are tested to confirm the theoretical aspects, demonstrate different evolutionary dynamics, and highlight the superiority of the novel developed algorithm compared to other existing analytical methods. For this purpose, associated graphs are displayed in two and three dimensions. Growing and decaying modes of the fractional parameters are analyzed for several α values. From a numerical viewpoint, the simulations and results declare that the proposed iterative algorithm is indeed straightforward and appropriate with efficiency for long-wavelength solutions of nonlinear partial differential equations. |
| first_indexed | 2024-04-11T09:22:22Z |
| format | Article |
| id | doaj.art-4137e42a96e1457bb23b91b90283ee17 |
| institution | Directory Open Access Journal |
| issn | 2314-8888 |
| language | English |
| last_indexed | 2024-04-11T09:22:22Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj.art-4137e42a96e1457bb23b91b90283ee172022-12-22T04:32:09ZengHindawi LimitedJournal of Function Spaces2314-88882022-01-01202210.1155/2022/4422186Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive MediaMohammed Al-Smadi0Shrideh Al-Omari1Yeliz Karaca2Shaher Momani3Department of Applied ScienceFaculty of Engineering TechnologyUniversity of Massachusetts Medical SchoolNonlinear Dynamics Research Center (NDRC)The aim of this paper is to investigate the approximate solutions of nonlinear temporal fractional models of Gardner and Cahn-Hilliard equations. The fractional models of the Gardner and Cahn-Hilliard equations play an important role in pulse propagation in dispersive media. The time-fractional derivative is observed in the conformable framework. In this orientation, a reliable computationally algorithm is designed and developed by following a residual error and multivariable power series expansion. Basically, the approximate solutions of pulse wave function of the fractional higher-order Gardner and Cahn-Hilliard equations are obtained in the form of a conformable convergent fractional series. Relevant consequences are theoretically and numerically investigated under the conformable sense. Besides, the analysis of the error and convergence of the developed technique are discussed. Some of the unidirectional homogeneous physical applications of the posed models in a finite compact regime are tested to confirm the theoretical aspects, demonstrate different evolutionary dynamics, and highlight the superiority of the novel developed algorithm compared to other existing analytical methods. For this purpose, associated graphs are displayed in two and three dimensions. Growing and decaying modes of the fractional parameters are analyzed for several α values. From a numerical viewpoint, the simulations and results declare that the proposed iterative algorithm is indeed straightforward and appropriate with efficiency for long-wavelength solutions of nonlinear partial differential equations.http://dx.doi.org/10.1155/2022/4422186 |
| spellingShingle | Mohammed Al-Smadi Shrideh Al-Omari Yeliz Karaca Shaher Momani Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive Media Journal of Function Spaces |
| title | Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive Media |
| title_full | Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive Media |
| title_fullStr | Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive Media |
| title_full_unstemmed | Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive Media |
| title_short | Effective Analytical Computational Technique for Conformable Time-Fractional Nonlinear Gardner Equation and Cahn-Hilliard Equations of Fourth and Sixth Order Emerging in Dispersive Media |
| title_sort | effective analytical computational technique for conformable time fractional nonlinear gardner equation and cahn hilliard equations of fourth and sixth order emerging in dispersive media |
| url | http://dx.doi.org/10.1155/2022/4422186 |
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