Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces
We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for a...
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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/10.1155/2013/262191 |
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| author | Mourad Kerboua Amar Debbouche Dumitru Baleanu |
| author_facet | Mourad Kerboua Amar Debbouche Dumitru Baleanu |
| author_sort | Mourad Kerboua |
| collection | DOAJ |
| description | We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory. |
| format | Article |
| id | doaj-art-b3e1b99a4d604ea3b806db2cb3431e56 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b3e1b99a4d604ea3b806db2cb3431e562025-08-20T03:20:51ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/262191262191Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert SpacesMourad Kerboua0Amar Debbouche1Dumitru Baleanu2Department of Mathematics, Guelma University, 24000 Guelma, AlgeriaDepartment of Mathematics, Guelma University, 24000 Guelma, AlgeriaDepartment of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi ArabiaWe study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.http://dx.doi.org/10.1155/2013/262191 |
| spellingShingle | Mourad Kerboua Amar Debbouche Dumitru Baleanu Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces Abstract and Applied Analysis |
| title | Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces |
| title_full | Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces |
| title_fullStr | Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces |
| title_full_unstemmed | Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces |
| title_short | Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces |
| title_sort | approximate controllability of sobolev type nonlocal fractional stochastic dynamic systems in hilbert spaces |
| url | http://dx.doi.org/10.1155/2013/262191 |
| work_keys_str_mv | AT mouradkerboua approximatecontrollabilityofsobolevtypenonlocalfractionalstochasticdynamicsystemsinhilbertspaces AT amardebbouche approximatecontrollabilityofsobolevtypenonlocalfractionalstochasticdynamicsystemsinhilbertspaces AT dumitrubaleanu approximatecontrollabilityofsobolevtypenonlocalfractionalstochasticdynamicsystemsinhilbertspaces |