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Fractional boundary value problems with Riemann-Liouville fractional derivatives.
- Source :
-
Advances in Difference Equations . 9/15/2015, Vol. 2015 Issue 1, p1-14. 14p. - Publication Year :
- 2015
-
Abstract
- In this paper, by employing two fixed point theorems of a sum operators, we investigate the existence and uniqueness of positive solutions for the following fractional boundary value problems: $-D_{0+}^{\alpha}x(t)=f(t, x(t), x(t))+g(t, x(t))$, $0< t <1$, $1< \alpha<2$, where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative, subject to either the boundary conditions $x(0)=x(1)=0$ or $x(0)=0$, $x(1)=\beta x(\eta)$ with $\eta, \beta\eta^{\alpha-1} \in(0,1)$. We also construct an iterative scheme to approximate the solution. As applications of the main results, two examples are given. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16871839
- Volume :
- 2015
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Advances in Difference Equations
- Publication Type :
- Academic Journal
- Accession number :
- 109465041
- Full Text :
- https://doi.org/10.1186/s13662-015-0413-y