Multiple Position Solutions For The Boundary Value Problem Of A Nonlinear Fractional Differential Equation

In this paper, we consider Green's function and its properties for the nonlinear fractional differential equation boundary value problemwhere 2<α≤3 is a real number, and D₀₊^αis the standard Riemann-Liouville differentiation.As an application of Green's function and its properties, we give some multiple positive solutions for singular and nonsingular boundary value problems, and also we give uniqueness of solution for singular problem by means of Leray-Shauder existence principle, a fixed-point theorem on cones and a mixed monotone method. Some concrete examples are respectively given to explain the above theorems finally.