Geodesic
Existence of positive solutions for singular fractional differential equations with integral boundary conditions
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     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/