The Solvability and Optimal Controls for Some Fractional Impulsive Equation
This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/914592 |
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| _version_ | 1832565668639145984 |
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| author | Xianghu Liu Zhenhai Liu Jiangfeng Han |
| author_facet | Xianghu Liu Zhenhai Liu Jiangfeng Han |
| author_sort | Xianghu Liu |
| collection | DOAJ |
| description | This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results. |
| format | Article |
| id | doaj-art-b70e17a5d1974c1a8849f34000457764 |
| 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-b70e17a5d1974c1a8849f340004577642025-02-03T01:07:03ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/914592914592The Solvability and Optimal Controls for Some Fractional Impulsive EquationXianghu Liu0Zhenhai Liu1Jiangfeng Han2School of Mathematics and Statistics, Central South University, Changsha, Hunan 410075, ChinaCollege of Sciences, Guangxi University for Nationalities Nanning, Guangxi 530006, ChinaFaculty of Mathematics and Computer Science, Jagiellonian University, ul. S. Lojasiewicza 6, 30-348 Krakow, PolandThis paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.http://dx.doi.org/10.1155/2013/914592 |
| spellingShingle | Xianghu Liu Zhenhai Liu Jiangfeng Han The Solvability and Optimal Controls for Some Fractional Impulsive Equation Abstract and Applied Analysis |
| title | The Solvability and Optimal Controls for Some Fractional Impulsive Equation |
| title_full | The Solvability and Optimal Controls for Some Fractional Impulsive Equation |
| title_fullStr | The Solvability and Optimal Controls for Some Fractional Impulsive Equation |
| title_full_unstemmed | The Solvability and Optimal Controls for Some Fractional Impulsive Equation |
| title_short | The Solvability and Optimal Controls for Some Fractional Impulsive Equation |
| title_sort | solvability and optimal controls for some fractional impulsive equation |
| url | http://dx.doi.org/10.1155/2013/914592 |
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