Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space
This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condit...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/585639 |
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| _version_ | 1832563731162202112 |
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| author | Bo Liu Yansheng Liu |
| author_facet | Bo Liu Yansheng Liu |
| author_sort | Bo Liu |
| collection | DOAJ |
| description | This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condition is established for the existence of at least two positive solutions to the approximate problem of the considered singular BVP. Second, using Ascoli-Arzela theorem, a sufficient condition is obtained for the existence of at least two positive solutions to the considered singular BVP from the convergent subsequence of the approximate problem. Finally, an illustrative example is given to support the obtained new results. |
| format | Article |
| id | doaj-art-c53eb237dd4f4b52a68dae1679b0a5bc |
| institution | Kabale University |
| 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-c53eb237dd4f4b52a68dae1679b0a5bc2025-02-03T01:12:41ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/585639585639Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach SpaceBo Liu0Yansheng Liu1Department of Mathematics, Shandong Normal University, Jinan 250014, ChinaDepartment of Mathematics, Shandong Normal University, Jinan 250014, ChinaThis paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condition is established for the existence of at least two positive solutions to the approximate problem of the considered singular BVP. Second, using Ascoli-Arzela theorem, a sufficient condition is obtained for the existence of at least two positive solutions to the considered singular BVP from the convergent subsequence of the approximate problem. Finally, an illustrative example is given to support the obtained new results.http://dx.doi.org/10.1155/2013/585639 |
| spellingShingle | Bo Liu Yansheng Liu Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space Journal of Function Spaces and Applications |
| title | Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space |
| title_full | Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space |
| title_fullStr | Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space |
| title_full_unstemmed | Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space |
| title_short | Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space |
| title_sort | positive solutions of a two point boundary value problem for singular fractional differential equations in banach space |
| url | http://dx.doi.org/10.1155/2013/585639 |
| work_keys_str_mv | AT boliu positivesolutionsofatwopointboundaryvalueproblemforsingularfractionaldifferentialequationsinbanachspace AT yanshengliu positivesolutionsofatwopointboundaryvalueproblemforsingularfractionaldifferentialequationsinbanachspace |