Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives
In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional dif...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
SpringerOpen
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/67081 |
| _version_ | 1848761470068719616 |
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| author | Liu, X. Liu, Lishan Wu, Yong Hong |
| author_facet | Liu, X. Liu, Lishan Wu, Yong Hong |
| author_sort | Liu, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional derivatives are considered under some appropriate conditions, and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable and it includes fractional derivatives. The existence of positive solutions for boundary conditions involving fractional derivatives is established. Finally, an example is given to demonstrate the validity of our main results. |
| first_indexed | 2025-11-14T10:32:11Z |
| format | Journal Article |
| id | curtin-20.500.11937-67081 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:32:11Z |
| publishDate | 2018 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-670812019-02-04T05:27:06Z Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives Liu, X. Liu, Lishan Wu, Yong Hong In this article, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation are obtained. Based on these properties and through the fixed point index theory, the singular nonlinear fractional differential equations with Riemann–Stieltjes integral boundary conditions involving fractional derivatives are considered under some appropriate conditions, and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable and it includes fractional derivatives. The existence of positive solutions for boundary conditions involving fractional derivatives is established. Finally, an example is given to demonstrate the validity of our main results. 2018 Journal Article http://hdl.handle.net/20.500.11937/67081 10.1186/s13661-018-0943-9 http://creativecommons.org/licenses/by/4.0/ SpringerOpen fulltext |
| spellingShingle | Liu, X. Liu, Lishan Wu, Yong Hong Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives |
| title | Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives |
| title_full | Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives |
| title_fullStr | Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives |
| title_full_unstemmed | Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives |
| title_short | Existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives |
| title_sort | existence of positive solutions for a singular nonlinear fractional differential equation with integral boundary conditions involving fractional derivatives |
| url | http://hdl.handle.net/20.500.11937/67081 |