Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spaces
The aim of the reported results in this manuscript is to handle the existence, uniqueness, extremal solutions, and Ulam-Hyers stability of solutions for a class of Ψ-Caputo fractional relaxation differential equations and a coupled system of Ψ-Caputo fractional relaxation differential equations in B...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/math.2021151?viewType=HTML |
| _version_ | 1818871036563685376 |
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| author | Choukri Derbazi Zidane Baitiche Mohammed S. Abdo Thabet Abdeljawad |
| author_facet | Choukri Derbazi Zidane Baitiche Mohammed S. Abdo Thabet Abdeljawad |
| author_sort | Choukri Derbazi |
| collection | DOAJ |
| description | The aim of the reported results in this manuscript is to handle the existence, uniqueness, extremal solutions, and Ulam-Hyers stability of solutions for a class of Ψ-Caputo fractional relaxation differential equations and a coupled system of Ψ-Caputo fractional relaxation differential equations in Banach spaces. The obtained results are derived by different methods of nonlinear analysis like the method of upper and lower solutions along with monotone iterative technique, Banach contraction principle, and Mönch's fixed point theorem concerted with the measures of noncompactness. Furthermore, the Ulam-Hyers stability of the proposed system is studied. Finally, two examples are presented to illustrate our theoretical findings. Our acquired results are recent in the frame of a Ψ-Caputo derivative with initial conditions in Banach spaces via the monotone iterative technique. As a results, we aim to fill this gap in the literature and contribute to enriching this academic area. |
| first_indexed | 2024-12-19T12:16:32Z |
| format | Article |
| id | doaj.art-349c66a352494a988bf39b455748a3e3 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T12:16:32Z |
| publishDate | 2021-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-349c66a352494a988bf39b455748a3e32022-12-21T20:21:57ZengAIMS PressAIMS Mathematics2473-69882021-01-01632486250910.3934/math.2021151Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spacesChoukri Derbazi0Zidane Baitiche 1Mohammed S. Abdo2Thabet Abdeljawad31. Laboratory of Mathematics and Applied Sciences University of Ghardaia, 47000, Algeria1. Laboratory of Mathematics and Applied Sciences University of Ghardaia, 47000, Algeria2. Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia 4. Department of Medical Research, China Medical University, Taichung 40402, Taiwan 5. Department of Computer Science and Information Engineering, Asia University, Taichung, TaiwanThe aim of the reported results in this manuscript is to handle the existence, uniqueness, extremal solutions, and Ulam-Hyers stability of solutions for a class of Ψ-Caputo fractional relaxation differential equations and a coupled system of Ψ-Caputo fractional relaxation differential equations in Banach spaces. The obtained results are derived by different methods of nonlinear analysis like the method of upper and lower solutions along with monotone iterative technique, Banach contraction principle, and Mönch's fixed point theorem concerted with the measures of noncompactness. Furthermore, the Ulam-Hyers stability of the proposed system is studied. Finally, two examples are presented to illustrate our theoretical findings. Our acquired results are recent in the frame of a Ψ-Caputo derivative with initial conditions in Banach spaces via the monotone iterative technique. As a results, we aim to fill this gap in the literature and contribute to enriching this academic area.http://www.aimspress.com/article/doi/10.3934/math.2021151?viewType=HTMLψ-caputo fractional derivativeextremal solutionsmonotone iterative techniqueupper and lower solutionsrelaxationulam-hyers stabilitybanach spaces |
| spellingShingle | Choukri Derbazi Zidane Baitiche Mohammed S. Abdo Thabet Abdeljawad Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spaces AIMS Mathematics ψ-caputo fractional derivative extremal solutions monotone iterative technique upper and lower solutions relaxation ulam-hyers stability banach spaces |
| title | Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spaces |
| title_full | Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spaces |
| title_fullStr | Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spaces |
| title_full_unstemmed | Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spaces |
| title_short | Qualitative analysis of fractional relaxation equation and coupled system with Ψ-Caputo fractional derivative in Banach spaces |
| title_sort | qualitative analysis of fractional relaxation equation and coupled system with ψ caputo fractional derivative in banach spaces |
| topic | ψ-caputo fractional derivative extremal solutions monotone iterative technique upper and lower solutions relaxation ulam-hyers stability banach spaces |
| url | http://www.aimspress.com/article/doi/10.3934/math.2021151?viewType=HTML |
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