Geodesic
Existence of positive solutions for singular fractional differential equations with integral boundary conditions
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 34B16, 34B18, 26A33
Keywords: Caputo derivative, fractional differential equations, positive solutions, integral boundary conditions, singular differential equation 
@article{EJDE_2012__2012__a95,
     author = {Jin,  Jingfu and Liu,  Xiping and Jia,  Mei},
     title = {Existence of positive solutions for singular fractional differential equations with integral boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1261.34005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a95/}
}
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Jin,  Jingfu; Liu,  Xiping; Jia,  Mei. Existence of positive solutions for singular fractional differential equations with integral boundary conditions. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a95/