Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions
We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/372749 |
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| author | Jessada Tariboon Sotiris K. Ntouyas Chatthai Thaiprayoon |
| author_facet | Jessada Tariboon Sotiris K. Ntouyas Chatthai Thaiprayoon |
| author_sort | Jessada Tariboon |
| collection | DOAJ |
| description | We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented. |
| format | Article |
| id | doaj-art-def44653cf3d4dfbbc14d31bcce07da1 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-def44653cf3d4dfbbc14d31bcce07da12025-02-03T01:04:01ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/372749372749Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral ConditionsJessada Tariboon0Sotiris K. Ntouyas1Chatthai Thaiprayoon2Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceNonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandWe study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’s fixed point theorem, Krasnoselskii’s fixed point theorem, Leray-Schauder’s nonlinear alternative, and Leray-Schauder’s degree theory. Enlightening examples illustrating the obtained results are also presented.http://dx.doi.org/10.1155/2014/372749 |
| spellingShingle | Jessada Tariboon Sotiris K. Ntouyas Chatthai Thaiprayoon Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions Advances in Mathematical Physics |
| title | Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions |
| title_full | Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions |
| title_fullStr | Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions |
| title_full_unstemmed | Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions |
| title_short | Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions |
| title_sort | nonlinear langevin equation of hadamard caputo type fractional derivatives with nonlocal fractional integral conditions |
| url | http://dx.doi.org/10.1155/2014/372749 |
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