Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation
We investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and co...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/986575 |
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| author | Moustafa El-Shahed Wafa M. Shammakh |
| author_facet | Moustafa El-Shahed Wafa M. Shammakh |
| author_sort | Moustafa El-Shahed |
| collection | DOAJ |
| description | We investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained. |
| format | Article |
| id | doaj-art-8a832dd0ec53429fa0e43ae295f4db15 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8a832dd0ec53429fa0e43ae295f4db152025-02-03T01:10:55ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/986575986575Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential EquationMoustafa El-Shahed0Wafa M. Shammakh1Department of Mathematics, Faculty of Arts and Sciences, College of Education, P.O. Box 3771, Qassim-Unizah 51911, Saudi ArabiaDepartment of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, P.O. Box 30903, Jeddah 21487, Saudi ArabiaWe investigate an m-point boundary value problem for nonlinear fractional differential equations. The associated Green function for the boundary value problem is given at first, and some useful properties of the Green function are obtained. By using the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem, the existence of multiple positive solutions is obtained.http://dx.doi.org/10.1155/2011/986575 |
| spellingShingle | Moustafa El-Shahed Wafa M. Shammakh Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation Abstract and Applied Analysis |
| title | Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_full | Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_fullStr | Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_full_unstemmed | Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_short | Existence of Positive Solutions for m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation |
| title_sort | existence of positive solutions for m point boundary value problem for nonlinear fractional differential equation |
| url | http://dx.doi.org/10.1155/2011/986575 |
| work_keys_str_mv | AT moustafaelshahed existenceofpositivesolutionsformpointboundaryvalueproblemfornonlinearfractionaldifferentialequation AT wafamshammakh existenceofpositivesolutionsformpointboundaryvalueproblemfornonlinearfractionaldifferentialequation |