On solutions of a class of three-point fractional boundary value problems
Abstract Existence results for the three-point fractional boundary value problem D α x ( t ) = f ( t , x ( t ) , D α − 1 x ( t ) ) , 0 < t < 1 , x ( 0 ) = A , x ( η ) − x ( 1 ) = ( η − 1 ) B , $$\begin{aligned}& D^{\alpha}x(t)= f \bigl(t, x(t), D^{\alpha-1} x(t) \bigr),\quad 0< t< 1,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-019-01319-x |
| _version_ | 1818575408251011072 |
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| author | Zhanbing Bai Yu Cheng Sujing Sun |
| author_facet | Zhanbing Bai Yu Cheng Sujing Sun |
| author_sort | Zhanbing Bai |
| collection | DOAJ |
| description | Abstract Existence results for the three-point fractional boundary value problem D α x ( t ) = f ( t , x ( t ) , D α − 1 x ( t ) ) , 0 < t < 1 , x ( 0 ) = A , x ( η ) − x ( 1 ) = ( η − 1 ) B , $$\begin{aligned}& D^{\alpha}x(t)= f \bigl(t, x(t), D^{\alpha-1} x(t) \bigr),\quad 0< t< 1, \\& x(0)=A, \qquad x(\eta)-x(1)=(\eta-1)B, \end{aligned}$$ are presented, where A , B ∈ R $A, B\in\mathbb{R}$ , 0 < η < 1 $0<\eta<1$ , 1 < α ≤ 2 $1<\alpha\leq2$ . D α x ( t ) $D^{\alpha}x(t)$ is the conformable fractional derivative, and f : [ 0 , 1 ] × R 2 → R $f: [0, 1]\times\mathbb{R}^{2}\to\mathbb{R}$ is continuous. The analysis is based on the nonlinear alternative of Leray–Schauder. |
| first_indexed | 2024-12-15T00:39:53Z |
| format | Article |
| id | doaj.art-b0360d6031a14b6c9fb132f8e0706c3a |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-15T00:39:53Z |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-b0360d6031a14b6c9fb132f8e0706c3a2022-12-21T22:41:41ZengSpringerOpenBoundary Value Problems1687-27702020-01-012020111210.1186/s13661-019-01319-xOn solutions of a class of three-point fractional boundary value problemsZhanbing Bai0Yu Cheng1Sujing Sun2College of Mathematics and System Science, Shandong University of Science and TechnologyCollege of Mathematics and System Science, Shandong University of Science and TechnologyCollege of Mathematics and System Science, Shandong University of Science and TechnologyAbstract Existence results for the three-point fractional boundary value problem D α x ( t ) = f ( t , x ( t ) , D α − 1 x ( t ) ) , 0 < t < 1 , x ( 0 ) = A , x ( η ) − x ( 1 ) = ( η − 1 ) B , $$\begin{aligned}& D^{\alpha}x(t)= f \bigl(t, x(t), D^{\alpha-1} x(t) \bigr),\quad 0< t< 1, \\& x(0)=A, \qquad x(\eta)-x(1)=(\eta-1)B, \end{aligned}$$ are presented, where A , B ∈ R $A, B\in\mathbb{R}$ , 0 < η < 1 $0<\eta<1$ , 1 < α ≤ 2 $1<\alpha\leq2$ . D α x ( t ) $D^{\alpha}x(t)$ is the conformable fractional derivative, and f : [ 0 , 1 ] × R 2 → R $f: [0, 1]\times\mathbb{R}^{2}\to\mathbb{R}$ is continuous. The analysis is based on the nonlinear alternative of Leray–Schauder.https://doi.org/10.1186/s13661-019-01319-xBoundary value problemsConformable fractional derivativeNonlinear alternative of Leray–Schauder |
| spellingShingle | Zhanbing Bai Yu Cheng Sujing Sun On solutions of a class of three-point fractional boundary value problems Boundary Value Problems Boundary value problems Conformable fractional derivative Nonlinear alternative of Leray–Schauder |
| title | On solutions of a class of three-point fractional boundary value problems |
| title_full | On solutions of a class of three-point fractional boundary value problems |
| title_fullStr | On solutions of a class of three-point fractional boundary value problems |
| title_full_unstemmed | On solutions of a class of three-point fractional boundary value problems |
| title_short | On solutions of a class of three-point fractional boundary value problems |
| title_sort | on solutions of a class of three point fractional boundary value problems |
| topic | Boundary value problems Conformable fractional derivative Nonlinear alternative of Leray–Schauder |
| url | https://doi.org/10.1186/s13661-019-01319-x |
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