On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra
Abstract This research investigates the dynamics of nonlinear coupled hybrid systems using a modified Mittag–Leffler fractional derivative. The primary objective is to establish criteria for the existence and uniqueness of solutions through the implementation of Dhage’s hybrid fixed-point theorem. T...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-12-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-81568-8 |
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| author | Mohammed A. Almalahi Khaled Aldwoah Faez Alqarni Manel Hleili Kamal Shah Fathea M. O. Birkea |
| author_facet | Mohammed A. Almalahi Khaled Aldwoah Faez Alqarni Manel Hleili Kamal Shah Fathea M. O. Birkea |
| author_sort | Mohammed A. Almalahi |
| collection | DOAJ |
| description | Abstract This research investigates the dynamics of nonlinear coupled hybrid systems using a modified Mittag–Leffler fractional derivative. The primary objective is to establish criteria for the existence and uniqueness of solutions through the implementation of Dhage’s hybrid fixed-point theorem. The study further analyzes the stability of the proposed model. To demonstrate the practical application of this framework, we utilize a modified Mittag–Leffler operator to model the transmission of the Ebola virus, known for its complex and diverse dynamics. The analysis is conducted using a combination of theoretical and numerical methods, including transforming the system of equations into an equivalent integral form, applying the fixed-point theorem, and developing a numerical scheme based on Lagrange’s interpolation for simulating the Ebola virus model. This study aims to enhance our understanding of Ebola virus dynamics and provide valuable insights for developing effective control strategies. |
| format | Article |
| id | doaj-art-3bfb7411de9446d08f936f228c991db7 |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-3bfb7411de9446d08f936f228c991db72025-08-20T02:48:27ZengNature PortfolioScientific Reports2045-23222024-12-0114111810.1038/s41598-024-81568-8On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebraMohammed A. Almalahi0Khaled Aldwoah1Faez Alqarni2Manel Hleili3Kamal Shah4Fathea M. O. Birkea5Department of Mathematics, Hajjah UniversityDepartment of Mathematics, Faculty of Science, Islamic University of MadinahDepartment of General Studies, University of Prince Mugrin (UPM)Department of mathematics, Faculty of Science, University of TabukDepartment of Mathematics, University of MalakandDepartment of Mathematics, Faculty of Science, Northern Border UniversityAbstract This research investigates the dynamics of nonlinear coupled hybrid systems using a modified Mittag–Leffler fractional derivative. The primary objective is to establish criteria for the existence and uniqueness of solutions through the implementation of Dhage’s hybrid fixed-point theorem. The study further analyzes the stability of the proposed model. To demonstrate the practical application of this framework, we utilize a modified Mittag–Leffler operator to model the transmission of the Ebola virus, known for its complex and diverse dynamics. The analysis is conducted using a combination of theoretical and numerical methods, including transforming the system of equations into an equivalent integral form, applying the fixed-point theorem, and developing a numerical scheme based on Lagrange’s interpolation for simulating the Ebola virus model. This study aims to enhance our understanding of Ebola virus dynamics and provide valuable insights for developing effective control strategies.https://doi.org/10.1038/s41598-024-81568-8Modified Mittag–Leffler-type derivativeCoupled hybrid systemsExistence and uniquenessStability analysisDhage’s hybrid fixed point theoremEbola virus model |
| spellingShingle | Mohammed A. Almalahi Khaled Aldwoah Faez Alqarni Manel Hleili Kamal Shah Fathea M. O. Birkea On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra Scientific Reports Modified Mittag–Leffler-type derivative Coupled hybrid systems Existence and uniqueness Stability analysis Dhage’s hybrid fixed point theorem Ebola virus model |
| title | On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra |
| title_full | On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra |
| title_fullStr | On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra |
| title_full_unstemmed | On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra |
| title_short | On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra |
| title_sort | on modified mittag leffler coupled hybrid fractional system constrained by dhage hybrid fixed point in banach algebra |
| topic | Modified Mittag–Leffler-type derivative Coupled hybrid systems Existence and uniqueness Stability analysis Dhage’s hybrid fixed point theorem Ebola virus model |
| url | https://doi.org/10.1038/s41598-024-81568-8 |
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