Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm
The objective of the manuscript is to model and analyze nonlinear waves dynamics through fuzzy-fractional calculus. Since fuzzy logic facilities the waves dynamics to be uncertain, while fractional calculus captures the memory effect inherent in wave propagation. The current study focuses on modelin...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-04-01
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| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447923005129 |
| _version_ | 1797243039012356096 |
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| author | Mubashir Qayyum Efaza Ahmad Ali Akgül Sayed M. El Din |
| author_facet | Mubashir Qayyum Efaza Ahmad Ali Akgül Sayed M. El Din |
| author_sort | Mubashir Qayyum |
| collection | DOAJ |
| description | The objective of the manuscript is to model and analyze nonlinear waves dynamics through fuzzy-fractional calculus. Since fuzzy logic facilities the waves dynamics to be uncertain, while fractional calculus captures the memory effect inherent in wave propagation. The current study focuses on modeling and analysis of fuzzy-fractional KdV equations namely Burgers KdV, Caudrey-Dodd-Gibbon KdV, and generalized KdV. To include uncertainty in the models, symmetric Gaussian fuzzy numbers are utilized in three different cases at upper and lower bounds in fractional environment. For numerical simulations, hybrid of Mahgoub transformation with homotopy perturbation is proposed and successfully implemented in fuzzy-fractional sense. Validity and competence of proposed methodology is confirmed theoretically by proving existence, uniqueness and convergence. The crest and trough in waves are analyzed in 2D and 3D simulations with respect to time, space, fractional parameter, and k-level sets. The obtained results highlight the accuracy of proposed methodology in case of nonlinear fuzzy-fractional waves dynamics and can be extended to other models in science and engineering. |
| first_indexed | 2024-04-24T18:48:46Z |
| format | Article |
| id | doaj.art-a915603419754dd3a754143179417a43 |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-04-24T18:48:46Z |
| publishDate | 2024-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-a915603419754dd3a754143179417a432024-03-27T04:51:50ZengElsevierAin Shams Engineering Journal2090-44792024-04-01154102623Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithmMubashir Qayyum0Efaza Ahmad1Ali Akgül2Sayed M. El Din3Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan; Corresponding author.Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, PakistanDepartment of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey; Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10 – TurkeyCenter of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, EgyptThe objective of the manuscript is to model and analyze nonlinear waves dynamics through fuzzy-fractional calculus. Since fuzzy logic facilities the waves dynamics to be uncertain, while fractional calculus captures the memory effect inherent in wave propagation. The current study focuses on modeling and analysis of fuzzy-fractional KdV equations namely Burgers KdV, Caudrey-Dodd-Gibbon KdV, and generalized KdV. To include uncertainty in the models, symmetric Gaussian fuzzy numbers are utilized in three different cases at upper and lower bounds in fractional environment. For numerical simulations, hybrid of Mahgoub transformation with homotopy perturbation is proposed and successfully implemented in fuzzy-fractional sense. Validity and competence of proposed methodology is confirmed theoretically by proving existence, uniqueness and convergence. The crest and trough in waves are analyzed in 2D and 3D simulations with respect to time, space, fractional parameter, and k-level sets. The obtained results highlight the accuracy of proposed methodology in case of nonlinear fuzzy-fractional waves dynamics and can be extended to other models in science and engineering.http://www.sciencedirect.com/science/article/pii/S2090447923005129Fuzzy fractional modelingSymmetric Gaussian fuzzy numbersKdV BurgersCaudrey-Dodd-Gibbon KdVSeventh order generalized KdVMahgoub transform |
| spellingShingle | Mubashir Qayyum Efaza Ahmad Ali Akgül Sayed M. El Din Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm Ain Shams Engineering Journal Fuzzy fractional modeling Symmetric Gaussian fuzzy numbers KdV Burgers Caudrey-Dodd-Gibbon KdV Seventh order generalized KdV Mahgoub transform |
| title | Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm |
| title_full | Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm |
| title_fullStr | Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm |
| title_full_unstemmed | Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm |
| title_short | Fuzzy-fractional modeling of Korteweg-de Vries equations in Gaussian-Caputo sense: New solutions via extended He-Mahgoub algorithm |
| title_sort | fuzzy fractional modeling of korteweg de vries equations in gaussian caputo sense new solutions via extended he mahgoub algorithm |
| topic | Fuzzy fractional modeling Symmetric Gaussian fuzzy numbers KdV Burgers Caudrey-Dodd-Gibbon KdV Seventh order generalized KdV Mahgoub transform |
| url | http://www.sciencedirect.com/science/article/pii/S2090447923005129 |
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