Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems
AbstractIn this paper, we delve into the analysis of the existence and stability concerning the [Formula: see text]-Mittag-Leffler-Ulam-Hyers within a particular class of coupled systems related to boundary value problems. These problems entail implicit nonlinear fractional differential equations an...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2024.2334130 |
| _version_ | 1797222241514029056 |
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| author | A. Salim C. Derbazi J. Alzabut A. Küçükaslan |
| author_facet | A. Salim C. Derbazi J. Alzabut A. Küçükaslan |
| author_sort | A. Salim |
| collection | DOAJ |
| description | AbstractIn this paper, we delve into the analysis of the existence and stability concerning the [Formula: see text]-Mittag-Leffler-Ulam-Hyers within a particular class of coupled systems related to boundary value problems. These problems entail implicit nonlinear fractional differential equations and [Formula: see text]-generalized ϑ-Hilfer fractional derivatives. To achieve our objectives, we employ the Mönch fixed point theorem, complemented by the application of the measure of noncompactness technique and an extension of the well-established Gronwall inequality. Furthermore, we include an illustrative example to showcase the practical utility of our results. The significance of our research lies in examining a comprehensive problem involving coupled systems, which serves as a generalization encompassing all the works mentioned in the introduction. It is viewed as a logical extension and continuation within the framework of this continually evolving theory. |
| first_indexed | 2024-04-24T13:18:12Z |
| format | Article |
| id | doaj.art-7007b0a005724420be493d7546adddf9 |
| institution | Directory Open Access Journal |
| issn | 2576-5299 |
| language | English |
| last_indexed | 2024-04-24T13:18:12Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj.art-7007b0a005724420be493d7546adddf92024-04-04T17:10:10ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992024-12-0131122524110.1080/25765299.2024.2334130Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systemsA. Salim0C. Derbazi1J. Alzabut2A. Küçükaslan3Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, Sidi Bel-Abbes, AlgeriaLaboratoire Equations Differentielles, Department of Mathematics, Faculty of Exact Sciences, University Frères Mentouri, Constantine, AlgeriaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Aerospace Engineering, Ankara Yıldırım Beyazıt University, Ankara, TürkiyeAbstractIn this paper, we delve into the analysis of the existence and stability concerning the [Formula: see text]-Mittag-Leffler-Ulam-Hyers within a particular class of coupled systems related to boundary value problems. These problems entail implicit nonlinear fractional differential equations and [Formula: see text]-generalized ϑ-Hilfer fractional derivatives. To achieve our objectives, we employ the Mönch fixed point theorem, complemented by the application of the measure of noncompactness technique and an extension of the well-established Gronwall inequality. Furthermore, we include an illustrative example to showcase the practical utility of our results. The significance of our research lies in examining a comprehensive problem involving coupled systems, which serves as a generalization encompassing all the works mentioned in the introduction. It is viewed as a logical extension and continuation within the framework of this continually evolving theory.https://www.tandfonline.com/doi/10.1080/25765299.2024.2334130Banach spacescoupled systemsexistencegeneralized Gronwall inequalitygeneralized Hilfer fractional derivativemeasure of noncompactness |
| spellingShingle | A. Salim C. Derbazi J. Alzabut A. Küçükaslan Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems Arab Journal of Basic and Applied Sciences Banach spaces coupled systems existence generalized Gronwall inequality generalized Hilfer fractional derivative measure of noncompactness |
| title | Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems |
| title_full | Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems |
| title_fullStr | Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems |
| title_full_unstemmed | Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems |
| title_short | Existence and κ-Mittag-Leffler-Ulam-Hyers stability results for implicit coupled (κ,ϑ)-fractional differential systems |
| title_sort | existence and κ mittag leffler ulam hyers stability results for implicit coupled κ ϑ fractional differential systems |
| topic | Banach spaces coupled systems existence generalized Gronwall inequality generalized Hilfer fractional derivative measure of noncompactness |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2024.2334130 |
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