Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions
In this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/2761321 |
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| _version_ | 1849411218804047872 |
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| author | Lizhen Chen Gang Li |
| author_facet | Lizhen Chen Gang Li |
| author_sort | Lizhen Chen |
| collection | DOAJ |
| description | In this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under the assumptions that the nonlocal item is compact continuous and Lipschitz continuous and multifunction is compact and Lipschitz, respectively. Our results extend the existence theorems for the classical Bagley-Torvik inclusion and some related models. |
| format | Article |
| id | doaj-art-6159dc3cbc7346a1bca54c616d913d3d |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-6159dc3cbc7346a1bca54c616d913d3d2025-08-20T03:34:49ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/27613212761321Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial ConditionsLizhen Chen0Gang Li1School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, ChinaSchool of Mathematical Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, ChinaIn this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under the assumptions that the nonlocal item is compact continuous and Lipschitz continuous and multifunction is compact and Lipschitz, respectively. Our results extend the existence theorems for the classical Bagley-Torvik inclusion and some related models.http://dx.doi.org/10.1155/2018/2761321 |
| spellingShingle | Lizhen Chen Gang Li Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions Journal of Function Spaces |
| title | Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions |
| title_full | Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions |
| title_fullStr | Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions |
| title_full_unstemmed | Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions |
| title_short | Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions |
| title_sort | existence results for generalized bagley torvik type fractional differential inclusions with nonlocal initial conditions |
| url | http://dx.doi.org/10.1155/2018/2761321 |
| work_keys_str_mv | AT lizhenchen existenceresultsforgeneralizedbagleytorviktypefractionaldifferentialinclusionswithnonlocalinitialconditions AT gangli existenceresultsforgeneralizedbagleytorviktypefractionaldifferentialinclusionswithnonlocalinitialconditions |