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Zbl 1228.34020
Staněk, Svatoslav
The existence of positive solutions of singular fractional boundary value problems.
(English)
[J] Comput. Math. Appl. 62, No. 3, 1379-1388 (2011). ISSN 0898-1221

Summary: We discuss the existence of positive solutions for the singular fractional boundary value problem $D^{\alpha }u+f(t,u,u',D^{\mu }u)=0$, $u(0)=0$, $u'(0)=u'(1)=0$, where $2<\alpha <3$, $0<\mu <1$. Here $D^{\alpha }$ is the standard Riemann-Liouville fractional derivative of order $\alpha$, $f$ is a Carathéodory function and $f(t,x,y,z)$ is singular at the value $0$ of its arguments $x,y,z$.
MSC 2000:
*34A08
34B99 Boundary value problems for ODE

Keywords: fractional differential equation; singular problem; Riemann-Liouville fractional derivative; Riemann-Liouville fractional integral; fixed point theorem on cones

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