Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation
We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0, 0<t<1, n-1<α≤n, n>3, u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the exi...
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| Main Authors: | , , |
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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/10.1155/2011/430457 |
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| _version_ | 1832545998621114368 |
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| author | Jinhua Wang Hongjun Xiang Yuling Zhao |
| author_facet | Jinhua Wang Hongjun Xiang Yuling Zhao |
| author_sort | Jinhua Wang |
| collection | DOAJ |
| description | We consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0, 0<t<1, n-1<α≤n, n>3, u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone, and concave. |
| format | Article |
| id | doaj-art-8599ba8240164938b886c775d136cd7e |
| 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-8599ba8240164938b886c775d136cd7e2025-02-03T07:24:12ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/430457430457Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential EquationJinhua Wang0Hongjun Xiang1Yuling Zhao2Department of Mathematics, Xiangnan University, Chenzhou 423000, ChinaDepartment of Mathematics, Xiangnan University, Chenzhou 423000, ChinaSchool of Mathematics and Computational Science, Sun-Yat Sen University, Guangzhou 510275, ChinaWe consider boundary value problem for nonlinear fractional differential equation D0+αu(t)+f(t,u(t))=0, 0<t<1, n-1<α≤n, n>3, u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, where D0+α denotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone, and concave.http://dx.doi.org/10.1155/2011/430457 |
| spellingShingle | Jinhua Wang Hongjun Xiang Yuling Zhao Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation Abstract and Applied Analysis |
| title | Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation |
| title_full | Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation |
| title_fullStr | Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation |
| title_full_unstemmed | Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation |
| title_short | Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation |
| title_sort | monotone and concave positive solutions to a boundary value problem for higher order fractional differential equation |
| url | http://dx.doi.org/10.1155/2011/430457 |
| work_keys_str_mv | AT jinhuawang monotoneandconcavepositivesolutionstoaboundaryvalueproblemforhigherorderfractionaldifferentialequation AT hongjunxiang monotoneandconcavepositivesolutionstoaboundaryvalueproblemforhigherorderfractionaldifferentialequation AT yulingzhao monotoneandconcavepositivesolutionstoaboundaryvalueproblemforhigherorderfractionaldifferentialequation |