A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces
In this paper, we study a coupled fully hybrid system of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold">k</mi><mo>,</mo><m...
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| Format: | Article |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1041 |
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| author | Abdellatif Boutiara Sina Etemad Sabri T. M. Thabet Sotiris K. Ntouyas Shahram Rezapour Jessada Tariboon |
| author_facet | Abdellatif Boutiara Sina Etemad Sabri T. M. Thabet Sotiris K. Ntouyas Shahram Rezapour Jessada Tariboon |
| author_sort | Abdellatif Boutiara |
| collection | DOAJ |
| description | In this paper, we study a coupled fully hybrid system of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold">k</mi><mo>,</mo><mi mathvariant="sans-serif">Φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>–Hilfer fractional differential equations equipped with non-symmetric <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold">k</mi><mo>,</mo><mi mathvariant="sans-serif">Φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>–Riemann-Liouville (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">RL</mi></semantics></math></inline-formula>) integral conditions. To prove the existence and uniqueness results, we use the Krasnoselskii and Perov fixed-point theorems with Lipschitzian matrix in the context of a generalized Banach space (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">GBS</mi></semantics></math></inline-formula>). Moreover, the Ulam–Hyers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">UH</mi></semantics></math></inline-formula>) stability of the solutions is discussed by using the Urs’s method. Finally, an illustrated example is given to confirm the validity of our results. |
| first_indexed | 2024-03-11T03:16:26Z |
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| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:26Z |
| publishDate | 2023-05-01 |
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| series | Symmetry |
| spelling | doaj.art-77520464b4f843b182e810c1bde5c3f22023-11-18T03:30:06ZengMDPI AGSymmetry2073-89942023-05-01155104110.3390/sym15051041A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach SpacesAbdellatif Boutiara0Sina Etemad1Sabri T. M. Thabet2Sotiris K. Ntouyas3Shahram Rezapour4Jessada Tariboon5Laboratory of Mathematics and Applied Sciences, University of Ghardaia, Ghardaia 47000, AlgeriaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, IranDepartment of Mathematics, University of Lahej, Lahej 73560, YemenDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, IranIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandIn this paper, we study a coupled fully hybrid system of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold">k</mi><mo>,</mo><mi mathvariant="sans-serif">Φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>–Hilfer fractional differential equations equipped with non-symmetric <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold">k</mi><mo>,</mo><mi mathvariant="sans-serif">Φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>–Riemann-Liouville (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">RL</mi></semantics></math></inline-formula>) integral conditions. To prove the existence and uniqueness results, we use the Krasnoselskii and Perov fixed-point theorems with Lipschitzian matrix in the context of a generalized Banach space (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">GBS</mi></semantics></math></inline-formula>). Moreover, the Ulam–Hyers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">UH</mi></semantics></math></inline-formula>) stability of the solutions is discussed by using the Urs’s method. Finally, an illustrated example is given to confirm the validity of our results.https://www.mdpi.com/2073-8994/15/5/1041(<b>k</b>, <b>Φ</b>)–Hilfer fractional derivativeexistencenonlinear analysisUlam stabilitygeneralized Banach spacesLipschitzian matrix |
| spellingShingle | Abdellatif Boutiara Sina Etemad Sabri T. M. Thabet Sotiris K. Ntouyas Shahram Rezapour Jessada Tariboon A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces Symmetry (<b>k</b>, <b>Φ</b>)–Hilfer fractional derivative existence nonlinear analysis Ulam stability generalized Banach spaces Lipschitzian matrix |
| title | A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces |
| title_full | A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces |
| title_fullStr | A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces |
| title_full_unstemmed | A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces |
| title_short | A Mathematical Theoretical Study of a Coupled Fully Hybrid (k, Φ)-Fractional Order System of BVPs in Generalized Banach Spaces |
| title_sort | mathematical theoretical study of a coupled fully hybrid k φ fractional order system of bvps in generalized banach spaces |
| topic | (<b>k</b>, <b>Φ</b>)–Hilfer fractional derivative existence nonlinear analysis Ulam stability generalized Banach spaces Lipschitzian matrix |
| url | https://www.mdpi.com/2073-8994/15/5/1041 |
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