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

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.