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

Abstract

© Vilnius University, 2016.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.