On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces
The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint,...
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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: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/428094 |
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| _version_ | 1850218611563560960 |
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| author | Hussein A. H. Salem Mieczysław Cichoń |
| author_facet | Hussein A. H. Salem Mieczysław Cichoń |
| author_sort | Hussein A. H. Salem |
| collection | DOAJ |
| description | The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given. |
| format | Article |
| id | doaj-art-31b09b66c3ca4f3593f07748bd1d0551 |
| institution | OA Journals |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-31b09b66c3ca4f3593f07748bd1d05512025-08-20T02:07:40ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/428094428094On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach SpacesHussein A. H. Salem0Mieczysław Cichoń1Department of Mathematics, Faculty of Sciences, Alexandria University, Alexandria, EgyptFaculty of Mathematics and Computer Science, Adam Mickiewcz University, Umultowska 87, 61-614 Poznan, PolandThe object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.http://dx.doi.org/10.1155/2013/428094 |
| spellingShingle | Hussein A. H. Salem Mieczysław Cichoń On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces Journal of Function Spaces and Applications |
| title | On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces |
| title_full | On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces |
| title_fullStr | On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces |
| title_full_unstemmed | On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces |
| title_short | On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces |
| title_sort | on solutions of fractional order boundary value problems with integral boundary conditions in banach spaces |
| url | http://dx.doi.org/10.1155/2013/428094 |
| work_keys_str_mv | AT husseinahsalem onsolutionsoffractionalorderboundaryvalueproblemswithintegralboundaryconditionsinbanachspaces AT mieczysławcichon onsolutionsoffractionalorderboundaryvalueproblemswithintegralboundaryconditionsinbanachspaces |