Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 63, pp. 1-14.

Title: Existence of positive solutions for singular fractional
       differential equations with integral boundary conditions

Authors: Jingfu Jin (Univ. of Shanghai for Science and Tech., China)
         Xiping Liu (Univ. of Shanghai for Science and Tech., China)
	 Mei Jia    (Univ. of Shanghai for Science and Tech., China)

Abstract:
 This article shows the  existence of a positive solution
 for the singular fractional differential equation with integral
 boundary condition
 $$\displaylines{
 {}^C\!D^p u(t)=\lambda h(t)f(t, u(t)), \quad t\in(0, 1), \cr
 u(0)-au(1)=\int^1_0g_0(s)u(s)\,ds, \cr
 u'(0)-b\,{}^C\!D^qu(1)=\int^1_0g_1(s)u(s)\,ds, \cr
 u''(0)=u'''(0)=\dots =u^{(n-1)}(0)=0,
 }$$
 where $\lambda $ is a parameter and the nonlinear term is allowed to 
 be singular  at $t=0, 1$ and $u=0$.
 We obtain an explicit interval for $\lambda$ such that for any $\lambda$ in
 this interval, existence of at least one positive solution is guaranteed.
 Our approach is by a fixed point theory  in cones combined with linear 
 operator  theory.	 


Submitted January 17, 2012. Published April 19, 2012.
Math Subject Classifications: 34B16, 34B18, 26A33
Key Words: Caputo derivative; fractional differential equations;
           positive solutions; integral boundary conditions;  
           singular differential equation