The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications
We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t)+f(t,u(t))+e(t)=0,0<t<1,u(0)=u'(0)=⋯=u(n-2)(0)=0,u(1)=βu(η), where n-1<α≤n,n≥3,0<β≤1,0≤η≤1, D0+α is the standard Riemann-Liouville derivative. Here our n...
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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/10.1155/2013/531038 |
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| author | Fuquan Jiang Xiaojie Xu Zhongwei Cao |
| author_facet | Fuquan Jiang Xiaojie Xu Zhongwei Cao |
| author_sort | Fuquan Jiang |
| collection | DOAJ |
| description | We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t)+f(t,u(t))+e(t)=0,0<t<1,u(0)=u'(0)=⋯=u(n-2)(0)=0,u(1)=βu(η), where n-1<α≤n,n≥3,0<β≤1,0≤η≤1, D0+α is the standard Riemann-Liouville derivative. Here our nonlinearity f may be singular at u=0. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem. |
| format | Article |
| id | doaj-art-1c224cf3caa244c784c060cf82252b6e |
| 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-1c224cf3caa244c784c060cf82252b6e2025-08-20T03:54:52ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/531038531038The Positive Properties of Green’s Function for Fractional Differential Equations and Its ApplicationsFuquan Jiang0Xiaojie Xu1Zhongwei Cao2The Department of Foundation, Harbin Finance University, Harbin 150030, ChinaCollege of Science, China University of Petroleum (East China), Qingdao 266580, ChinaDepartment of Applied Mathematics, Changchun Taxation College, Changchun 130117, ChinaWe consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t)+f(t,u(t))+e(t)=0,0<t<1,u(0)=u'(0)=⋯=u(n-2)(0)=0,u(1)=βu(η), where n-1<α≤n,n≥3,0<β≤1,0≤η≤1, D0+α is the standard Riemann-Liouville derivative. Here our nonlinearity f may be singular at u=0. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.http://dx.doi.org/10.1155/2013/531038 |
| spellingShingle | Fuquan Jiang Xiaojie Xu Zhongwei Cao The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications Abstract and Applied Analysis |
| title | The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications |
| title_full | The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications |
| title_fullStr | The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications |
| title_full_unstemmed | The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications |
| title_short | The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications |
| title_sort | positive properties of green s function for fractional differential equations and its applications |
| url | http://dx.doi.org/10.1155/2013/531038 |
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