Analytical study of ABC-fractional pantograph implicit differential equation with respect to another function
This article aims to establish sufficient conditions for qualitative properties of the solutions for a new class of a pantograph implicit system in the framework of Atangana-Baleanu-Caputo ($ \mathcal{ABC} $) fractional derivatives with respect to another function under integral boundary conditions....
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231202?viewType=HTML |
| _version_ | 1797743001684934656 |
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| author | Sabri T. M. Thabet Miguel Vivas-Cortez Imed Kedim |
| author_facet | Sabri T. M. Thabet Miguel Vivas-Cortez Imed Kedim |
| author_sort | Sabri T. M. Thabet |
| collection | DOAJ |
| description | This article aims to establish sufficient conditions for qualitative properties of the solutions for a new class of a pantograph implicit system in the framework of Atangana-Baleanu-Caputo ($ \mathcal{ABC} $) fractional derivatives with respect to another function under integral boundary conditions. The Schaefer and Banach fixed point theorems (FPTs) are utilized to investigate the existence and uniqueness results for this pantograph implicit system. Moreover, some stability types such as the Ulam-Hyers $ (\mathbb{UH}) $, generalized $ \mathbb{UH} $, Ulam-Hyers-Rassias $ (\mathbb{UHR}) $ and generalized $ \mathbb{UHR} $ are discussed. Finally, interpretation mathematical examples are given in order to guarantee the validity of the main findings. Moreover, the fractional operator used in this study is more generalized and supports our results to be more extensive and covers several new and existing problems in the literature. |
| first_indexed | 2024-03-12T14:48:18Z |
| format | Article |
| id | doaj.art-e17e63cb2d5a42c0965a8b86bfe1a430 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T14:48:18Z |
| publishDate | 2023-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e17e63cb2d5a42c0965a8b86bfe1a4302023-08-16T01:24:34ZengAIMS PressAIMS Mathematics2473-69882023-07-01810236352365410.3934/math.20231202Analytical study of ABC-fractional pantograph implicit differential equation with respect to another functionSabri T. M. Thabet0Miguel Vivas-Cortez1Imed Kedim 21. Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen2. Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador3. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaThis article aims to establish sufficient conditions for qualitative properties of the solutions for a new class of a pantograph implicit system in the framework of Atangana-Baleanu-Caputo ($ \mathcal{ABC} $) fractional derivatives with respect to another function under integral boundary conditions. The Schaefer and Banach fixed point theorems (FPTs) are utilized to investigate the existence and uniqueness results for this pantograph implicit system. Moreover, some stability types such as the Ulam-Hyers $ (\mathbb{UH}) $, generalized $ \mathbb{UH} $, Ulam-Hyers-Rassias $ (\mathbb{UHR}) $ and generalized $ \mathbb{UHR} $ are discussed. Finally, interpretation mathematical examples are given in order to guarantee the validity of the main findings. Moreover, the fractional operator used in this study is more generalized and supports our results to be more extensive and covers several new and existing problems in the literature. https://www.aimspress.com/article/doi/10.3934/math.20231202?viewType=HTMLfractional differential equationsfractional calculus with respect to another functionnon-singular fractional operatorsexistence and uniqueness results |
| spellingShingle | Sabri T. M. Thabet Miguel Vivas-Cortez Imed Kedim Analytical study of ABC-fractional pantograph implicit differential equation with respect to another function AIMS Mathematics fractional differential equations fractional calculus with respect to another function non-singular fractional operators existence and uniqueness results |
| title | Analytical study of ABC-fractional pantograph implicit differential equation with respect to another function |
| title_full | Analytical study of ABC-fractional pantograph implicit differential equation with respect to another function |
| title_fullStr | Analytical study of ABC-fractional pantograph implicit differential equation with respect to another function |
| title_full_unstemmed | Analytical study of ABC-fractional pantograph implicit differential equation with respect to another function |
| title_short | Analytical study of ABC-fractional pantograph implicit differential equation with respect to another function |
| title_sort | analytical study of abc fractional pantograph implicit differential equation with respect to another function |
| topic | fractional differential equations fractional calculus with respect to another function non-singular fractional operators existence and uniqueness results |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231202?viewType=HTML |
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