Geodesic
Existence and uniqueness of positive solutions to higher-order nonlinear fractional differential equation with integral boundary conditions
Electronic journal of differential equations, Tome 2012 (2012)
In this article, we consider the nonlinear fractional order three-point boundary-value problem

$\displaylines{ D_{0+}^{\alpha} u(t) + f(t,u(t))=0, \quad 0 t 1,\cr u(0) = u'(0) = \dots = u^{(n-2)}(0)=0, \quad u^{(n-2)}(1) = \int_0^\eta u(s)ds, }$

where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative, $n-1 \alpha \leq n, n \geq 3$. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions to the above boundary value problem.
Classification : 26A33, 34B18, 34B27
Keywords: partially ordered sets, fixed-point theorem, positive solution 
@article{EJDE_2012__2012__a2,
     author = {Zhou,  Chenxing},
     title = {Existence and uniqueness of positive solutions to higher-order nonlinear fractional differential equation with integral boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1290.26011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a2/}
}
TY  - JOUR
AU  - Zhou,  Chenxing
TI  - Existence and uniqueness of positive solutions to higher-order nonlinear fractional differential equation with integral boundary conditions
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a2/
LA  - en
ID  - EJDE_2012__2012__a2
ER  - 
%0 Journal Article
%A Zhou,  Chenxing
%T Existence and uniqueness of positive solutions to higher-order nonlinear fractional differential equation with integral boundary conditions
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a2/
%G en
%F EJDE_2012__2012__a2
Zhou,  Chenxing. Existence and uniqueness of positive solutions to higher-order nonlinear fractional differential equation with integral boundary conditions. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a2/