Existence results for fractional differential equations with integral and multi-point boundary conditions
Abstract This paper concerns a new kind of fractional differential equation of arbitrary order by combining a multi-point boundary condition with an integral boundary condition. By solving the equation which is equivalent to the problem we are going to investigate, the Green’s functions are obtained...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-017-0924-4 |
| _version_ | 1818143301909348352 |
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| author | Youyu Wang Shuilian Liang Qichao Wang |
| author_facet | Youyu Wang Shuilian Liang Qichao Wang |
| author_sort | Youyu Wang |
| collection | DOAJ |
| description | Abstract This paper concerns a new kind of fractional differential equation of arbitrary order by combining a multi-point boundary condition with an integral boundary condition. By solving the equation which is equivalent to the problem we are going to investigate, the Green’s functions are obtained. By defining a continuous operator on a Banach space and taking advantage of the cone theory and some fixed point theorems, the existence of multiple positive solutions for the BVPs is proved based on some properties of Green’s functions and under the circumstance that the continuous functions f satisfy certain hypothesis. Finally, examples are provided to illustrate the results. |
| first_indexed | 2024-12-11T11:29:30Z |
| format | Article |
| id | doaj.art-64846d578c16446cb85a76ef7b4e13f6 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-11T11:29:30Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-64846d578c16446cb85a76ef7b4e13f62022-12-22T01:08:54ZengSpringerOpenBoundary Value Problems1687-27702018-01-012018111110.1186/s13661-017-0924-4Existence results for fractional differential equations with integral and multi-point boundary conditionsYouyu Wang0Shuilian Liang1Qichao Wang2Department of Mathematics, Tianjin University of Finance and EconomicsDepartment of Mathematics, Tianjin University of Finance and EconomicsDepartment of Mathematics, Tianjin University of Finance and EconomicsAbstract This paper concerns a new kind of fractional differential equation of arbitrary order by combining a multi-point boundary condition with an integral boundary condition. By solving the equation which is equivalent to the problem we are going to investigate, the Green’s functions are obtained. By defining a continuous operator on a Banach space and taking advantage of the cone theory and some fixed point theorems, the existence of multiple positive solutions for the BVPs is proved based on some properties of Green’s functions and under the circumstance that the continuous functions f satisfy certain hypothesis. Finally, examples are provided to illustrate the results.http://link.springer.com/article/10.1186/s13661-017-0924-4fractional differential equationboundary value problemGreen’s functionfixed point theorems |
| spellingShingle | Youyu Wang Shuilian Liang Qichao Wang Existence results for fractional differential equations with integral and multi-point boundary conditions Boundary Value Problems fractional differential equation boundary value problem Green’s function fixed point theorems |
| title | Existence results for fractional differential equations with integral and multi-point boundary conditions |
| title_full | Existence results for fractional differential equations with integral and multi-point boundary conditions |
| title_fullStr | Existence results for fractional differential equations with integral and multi-point boundary conditions |
| title_full_unstemmed | Existence results for fractional differential equations with integral and multi-point boundary conditions |
| title_short | Existence results for fractional differential equations with integral and multi-point boundary conditions |
| title_sort | existence results for fractional differential equations with integral and multi point boundary conditions |
| topic | fractional differential equation boundary value problem Green’s function fixed point theorems |
| url | http://link.springer.com/article/10.1186/s13661-017-0924-4 |
| work_keys_str_mv | AT youyuwang existenceresultsforfractionaldifferentialequationswithintegralandmultipointboundaryconditions AT shuilianliang existenceresultsforfractionaldifferentialequationswithintegralandmultipointboundaryconditions AT qichaowang existenceresultsforfractionaldifferentialequationswithintegralandmultipointboundaryconditions |