A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition
We deal with nonlocal boundary value problems of fractional equations of Volterra type involving Riemann-Liouville derivative. Firstly, by defining a weighted norm and using the Banach fixed point theorem, we show the existence and uniqueness of solutions. Then, we obtain the existence of extremal s...
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| Main Authors: | , |
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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/10.1155/2013/432941 |
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| _version_ | 1832554662238093312 |
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| author | Zhenhai Liu Rui Wang |
| author_facet | Zhenhai Liu Rui Wang |
| author_sort | Zhenhai Liu |
| collection | DOAJ |
| description | We deal with nonlocal boundary value problems of fractional equations of Volterra type involving Riemann-Liouville derivative. Firstly, by defining a weighted norm and using the Banach fixed point theorem, we show the existence and uniqueness of solutions. Then, we obtain the existence of extremal solutions by use of the monotone iterative technique. Finally, an example illustrates the results. |
| format | Article |
| id | doaj-art-c1233892879942fbbcddab3f2e5b5ab0 |
| 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-c1233892879942fbbcddab3f2e5b5ab02025-02-03T05:51:00ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/432941432941A Note on Fractional Equations of Volterra Type with Nonlocal Boundary ConditionZhenhai Liu0Rui Wang1Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, ChinaCollege of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, ChinaWe deal with nonlocal boundary value problems of fractional equations of Volterra type involving Riemann-Liouville derivative. Firstly, by defining a weighted norm and using the Banach fixed point theorem, we show the existence and uniqueness of solutions. Then, we obtain the existence of extremal solutions by use of the monotone iterative technique. Finally, an example illustrates the results.http://dx.doi.org/10.1155/2013/432941 |
| spellingShingle | Zhenhai Liu Rui Wang A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition Abstract and Applied Analysis |
| title | A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition |
| title_full | A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition |
| title_fullStr | A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition |
| title_full_unstemmed | A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition |
| title_short | A Note on Fractional Equations of Volterra Type with Nonlocal Boundary Condition |
| title_sort | note on fractional equations of volterra type with nonlocal boundary condition |
| url | http://dx.doi.org/10.1155/2013/432941 |
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