Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator
In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. The results presented in this study establish the existence, uniqueness, and Hyers–Ula...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/2288477 |
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| author | Sombir Dhaniya Anoop Kumar Aziz Khan Thabet Abdeljawad Manar A. Alqudah |
| author_facet | Sombir Dhaniya Anoop Kumar Aziz Khan Thabet Abdeljawad Manar A. Alqudah |
| author_sort | Sombir Dhaniya |
| collection | DOAJ |
| description | In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. The results presented in this study establish the existence, uniqueness, and Hyers–Ulam (HU) stability of the solution to the proposed equation. We achieved our main result by using the Banach contraction mapping principle and Krasonoselskii’s fixed point theorem. Furthermore, we introduce an application to demonstrate the validity of the results of our findings. |
| format | Article |
| id | doaj-art-a0509de7f5484a67bcc15891da2cc814 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-a0509de7f5484a67bcc15891da2cc8142025-02-03T06:42:57ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/2288477Existence Results of Langevin Equations with Caputo–Hadamard Fractional OperatorSombir Dhaniya0Anoop Kumar1Aziz Khan2Thabet Abdeljawad3Manar A. Alqudah4Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsDepartment of Mathematics and SciencesDepartment of Mathematics and SciencesDepartment of Mathematical SciencesIn this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. The results presented in this study establish the existence, uniqueness, and Hyers–Ulam (HU) stability of the solution to the proposed equation. We achieved our main result by using the Banach contraction mapping principle and Krasonoselskii’s fixed point theorem. Furthermore, we introduce an application to demonstrate the validity of the results of our findings.http://dx.doi.org/10.1155/2023/2288477 |
| spellingShingle | Sombir Dhaniya Anoop Kumar Aziz Khan Thabet Abdeljawad Manar A. Alqudah Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator Journal of Mathematics |
| title | Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator |
| title_full | Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator |
| title_fullStr | Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator |
| title_full_unstemmed | Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator |
| title_short | Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator |
| title_sort | existence results of langevin equations with caputo hadamard fractional operator |
| url | http://dx.doi.org/10.1155/2023/2288477 |
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