Nonlinear Analysis: Modelling and Control
Vol. 21, No. 5
Limin Guo, Lishan Liu, Yonghong Wu
Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions
doi:10.15388/NA.2016.5.5
Received  2015-01-08  /   Revised  2015-08-04  /   Accepted   2015-07-01
Published Online  2016-06-23
Abstract
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.
Keywords:
Caputo's fractional differential equation, positive solution, Green's function, Avery–
Peterson's fixed point theorem.