An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions
Abstract In this manuscript, we focus our attention on investigating new Lyapunov-type inequalities (LTIs) for two classes of boundary value problems (BVPs) in the framework of Katugampola–Hilfer fractional derivatives, supplemented by nonlocal, integral, and mixed boundary conditions. The equivalen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-03070-5 |
| _version_ | 1797376733149659136 |
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| author | Sabri T. M. Thabet Imed Kedim |
| author_facet | Sabri T. M. Thabet Imed Kedim |
| author_sort | Sabri T. M. Thabet |
| collection | DOAJ |
| description | Abstract In this manuscript, we focus our attention on investigating new Lyapunov-type inequalities (LTIs) for two classes of boundary value problems (BVPs) in the framework of Katugampola–Hilfer fractional derivatives, supplemented by nonlocal, integral, and mixed boundary conditions. The equivalent integral equations of the proposed Katugampola–Hilfer fractional BVPs are established in the context of Green functions. Also, the properties of these Green functions are proved. The LTIs are investigated as sufficient criteria for the existence and nonexistence of nontrivial solutions for the subjected problems. Our systems are more general than in the literature, as a consequence there are many new and known specific cases included. Finally, our results are applied for estimating eigenvalues of two given BVPs. |
| first_indexed | 2024-03-08T19:43:57Z |
| format | Article |
| id | doaj.art-e61c82c032d1463a81c3d8dec615bdb6 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-08T19:43:57Z |
| publishDate | 2023-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-e61c82c032d1463a81c3d8dec615bdb62023-12-24T12:32:05ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-12-012023112210.1186/s13660-023-03070-5An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditionsSabri T. M. Thabet0Imed Kedim1Department of Mathematics, Radfan University College, University of LahejDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz UniversityAbstract In this manuscript, we focus our attention on investigating new Lyapunov-type inequalities (LTIs) for two classes of boundary value problems (BVPs) in the framework of Katugampola–Hilfer fractional derivatives, supplemented by nonlocal, integral, and mixed boundary conditions. The equivalent integral equations of the proposed Katugampola–Hilfer fractional BVPs are established in the context of Green functions. Also, the properties of these Green functions are proved. The LTIs are investigated as sufficient criteria for the existence and nonexistence of nontrivial solutions for the subjected problems. Our systems are more general than in the literature, as a consequence there are many new and known specific cases included. Finally, our results are applied for estimating eigenvalues of two given BVPs.https://doi.org/10.1186/s13660-023-03070-5Fractional boundary value problemKatugampola–Hilfer fractional derivativeExistence and nonexistence solutionsLyapunov-type inequality |
| spellingShingle | Sabri T. M. Thabet Imed Kedim An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions Journal of Inequalities and Applications Fractional boundary value problem Katugampola–Hilfer fractional derivative Existence and nonexistence solutions Lyapunov-type inequality |
| title | An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions |
| title_full | An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions |
| title_fullStr | An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions |
| title_full_unstemmed | An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions |
| title_short | An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions |
| title_sort | investigation of a new lyapunov type inequality for katugampola hilfer fractional bvp with nonlocal and integral boundary conditions |
| topic | Fractional boundary value problem Katugampola–Hilfer fractional derivative Existence and nonexistence solutions Lyapunov-type inequality |
| url | https://doi.org/10.1186/s13660-023-03070-5 |
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