Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions

Limin Guo, Lishan Liu, Yonghong Wu
2016 Nonlinear Analysis: Modelling and Control  
In this paper, we investigate the existence of at least three positive solutions to a singular boundary value problem of Caputo's fractional differential equations with a boundary condition involving values at infinite number of points. Firstly, we establish Green's function and its properties. Then the existence of multiple positive solutions is obtained by Avery-Peterson's fixed point theorem. Finally, an example is given to demonstrate the application of our main results. . , u (i) (t) = 0,
more » ... . , u (i) (t) = 0, 0 < t < 1, u(0) = u (0) = · · · = u (i−1) (0) = u (i+1) (0) = · · · = u (n−1) (0) = 0, u (i) (1) = 0,
doi:10.15388/na.2016.5.5 fatcat:wvs3iufjgrhafejvi6u5jfo52y