Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives
We study the singular fractional-order boundary-value problem with a sign-changing nonlinear term -??????(??)=??(??)??(??,??(??),????1??(??),????2??(??),…,??????-1??(??)),0<??<1,????????(0)=0,1=??=??-1,??????-1+1??(0)=0, ??????-1???(1)=??-2??=1??????????-1??(????), where ??-1<??...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Hindawi Publishing Corporation
2012
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| Online Access: | http://www.hindawi.com/journals/aaa/2012/797398/ http://hdl.handle.net/20.500.11937/47089 |
| _version_ | 1848757738212950016 |
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| author | Wu, T. Zhang, Xinguang Lu, Y. |
| author_facet | Wu, T. Zhang, Xinguang Lu, Y. |
| author_sort | Wu, T. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We study the singular fractional-order boundary-value problem with a sign-changing nonlinear term -??????(??)=??(??)??(??,??(??),????1??(??),????2??(??),…,??????-1??(??)),0<??<1,????????(0)=0,1=??=??-1,??????-1+1??(0)=0, ??????-1???(1)=??-2??=1??????????-1??(????), where ??-1<??=??, ???N and ??=3 with 0<??1<??2<?<????-2<????-1 and ??-3<????-1<??-2, ?????R,0<??1<??2<?<????-2<1 satisfying ?0<??-2??=1????????-????-1??-1<1, ???? is the standard Riemann-Liouville derivative, ??:[0,1]×R???R is a sign-changing continuous function and may be unbounded from below with respect to ????, and ??:(0,1)?[0,8) is continuous. Some new results on the existence of nontrivial solutions for the above problem are obtained by computing the topological degree of a completely continuous field. |
| first_indexed | 2025-11-14T09:32:52Z |
| format | Journal Article |
| id | curtin-20.500.11937-47089 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:32:52Z |
| publishDate | 2012 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-470892018-12-14T00:54:42Z Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives Wu, T. Zhang, Xinguang Lu, Y. We study the singular fractional-order boundary-value problem with a sign-changing nonlinear term -??????(??)=??(??)??(??,??(??),????1??(??),????2??(??),…,??????-1??(??)),0<??<1,????????(0)=0,1=??=??-1,??????-1+1??(0)=0, ??????-1???(1)=??-2??=1??????????-1??(????), where ??-1<??=??, ???N and ??=3 with 0<??1<??2<?<????-2<????-1 and ??-3<????-1<??-2, ?????R,0<??1<??2<?<????-2<1 satisfying ?0<??-2??=1????????-????-1??-1<1, ???? is the standard Riemann-Liouville derivative, ??:[0,1]×R???R is a sign-changing continuous function and may be unbounded from below with respect to ????, and ??:(0,1)?[0,8) is continuous. Some new results on the existence of nontrivial solutions for the above problem are obtained by computing the topological degree of a completely continuous field. 2012 Journal Article http://hdl.handle.net/20.500.11937/47089 http://www.hindawi.com/journals/aaa/2012/797398/ Hindawi Publishing Corporation restricted |
| spellingShingle | Wu, T. Zhang, Xinguang Lu, Y. Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives |
| title | Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives |
| title_full | Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives |
| title_fullStr | Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives |
| title_full_unstemmed | Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives |
| title_short | Solutions of Sign-Changing Fractional Differential Equation with the Fractional Derivatives |
| title_sort | solutions of sign-changing fractional differential equation with the fractional derivatives |
| url | http://www.hindawi.com/journals/aaa/2012/797398/ http://hdl.handle.net/20.500.11937/47089 |