Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations
We consider the control systems governed by semilinear differential equations with Riemann-Liouville fractional derivatives in Banach spaces. Firstly, by applying fixed point strategy, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad cl...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/216919 |
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| author | Xue Pan Xiuwen Li Jing Zhao |
| author_facet | Xue Pan Xiuwen Li Jing Zhao |
| author_sort | Xue Pan |
| collection | DOAJ |
| description | We consider the control systems governed by semilinear differential equations with Riemann-Liouville fractional derivatives in Banach spaces. Firstly, by applying fixed point strategy, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of fractional infinite dimensional control systems. Then, by using generally mild conditions of cost functional, we extend the existence result of optimal controls to the Riemann-Liouville fractional control systems. Finally, a concrete application is given to illustrate the effectiveness of our main results. |
| format | Article |
| id | doaj-art-5b61ebd9109a4a5a9b4b9bc414086fee |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5b61ebd9109a4a5a9b4b9bc414086fee2025-02-03T01:26:18ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/216919216919Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential EquationsXue Pan0Xiuwen Li1Jing Zhao2College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaCollege of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaCollege of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaWe consider the control systems governed by semilinear differential equations with Riemann-Liouville fractional derivatives in Banach spaces. Firstly, by applying fixed point strategy, some suitable conditions are established to guarantee the existence and uniqueness of mild solutions for a broad class of fractional infinite dimensional control systems. Then, by using generally mild conditions of cost functional, we extend the existence result of optimal controls to the Riemann-Liouville fractional control systems. Finally, a concrete application is given to illustrate the effectiveness of our main results.http://dx.doi.org/10.1155/2014/216919 |
| spellingShingle | Xue Pan Xiuwen Li Jing Zhao Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations Abstract and Applied Analysis |
| title | Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations |
| title_full | Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations |
| title_fullStr | Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations |
| title_full_unstemmed | Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations |
| title_short | Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations |
| title_sort | solvability and optimal controls of semilinear riemann liouville fractional differential equations |
| url | http://dx.doi.org/10.1155/2014/216919 |
| work_keys_str_mv | AT xuepan solvabilityandoptimalcontrolsofsemilinearriemannliouvillefractionaldifferentialequations AT xiuwenli solvabilityandoptimalcontrolsofsemilinearriemannliouvillefractionaldifferentialequations AT jingzhao solvabilityandoptimalcontrolsofsemilinearriemannliouvillefractionaldifferentialequations |