Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions
We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce the PC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secon...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/639492 |
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| _version_ | 1832559033646579712 |
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| author | Zhenhai Liu Maojun Bin |
| author_facet | Zhenhai Liu Maojun Bin |
| author_sort | Zhenhai Liu |
| collection | DOAJ |
| description | We study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce the PC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results. |
| format | Article |
| id | doaj-art-ceb13df45c5d4818add925be1f567e33 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ceb13df45c5d4818add925be1f567e332025-02-03T01:31:01ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/639492639492Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential InclusionsZhenhai Liu0Maojun Bin1Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaGuangxi Key Laboratory of Hybrid Computation and IC Design Analysis, College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaWe study the control systems governed by impulsive Riemann-Liouville fractional differential inclusions and their approximate controllability in Banach space. Firstly, we introduce the PC1-α-mild solutions for the impulsive Riemann-Liouville fractional differential inclusions in Banach spaces. Secondly, by using the fractional power of operators and a fixed point theorem for multivalued maps, we establish sufficient conditions for the approximate controllability for a class of Riemann-Liouville fractional impulsive differential inclusions, which is a generalization and continuation of the recent results on this issue. At the end, we give an example to illustrate the application of the abstract results.http://dx.doi.org/10.1155/2013/639492 |
| spellingShingle | Zhenhai Liu Maojun Bin Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions Abstract and Applied Analysis |
| title | Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions |
| title_full | Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions |
| title_fullStr | Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions |
| title_full_unstemmed | Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions |
| title_short | Approximate Controllability for Impulsive Riemann-Liouville Fractional Differential Inclusions |
| title_sort | approximate controllability for impulsive riemann liouville fractional differential inclusions |
| url | http://dx.doi.org/10.1155/2013/639492 |
| work_keys_str_mv | AT zhenhailiu approximatecontrollabilityforimpulsiveriemannliouvillefractionaldifferentialinclusions AT maojunbin approximatecontrollabilityforimpulsiveriemannliouvillefractionaldifferentialinclusions |