The Positive Solutions For Boundary Value Problems Of Fractional Differential Equations

In this paper, we mainly talk about the existence of positive solutions for three types of fractional differential equations.Firstly, we prove the existences of at least one or multiple of positive solutions for a class of nonlinear fractioanl euqation with its order number greater than three and less than or equal to four. Bying using Guo-krasnoselskii fixed point theroem and Leggett-Williams fixed point theroem, we obtain the existence of positive solutions. The proporties of Green’s function is the key to the coclusion. Two examples are given to illustrate the main results.Secondly, by using Guo-krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem, we obtain the existence of positive solutions for a three-point boundary value problem with fractional differential equations. The properties of the corresponding Green’s function is the key of this results. Then, two examples to demonstrate the main results.Finaly, we study the boundary value problem with p-Laplacian operator, we prove the existence and nonexistence of positive solutions for this fractional differential equation. The range of parameter is the key to the conculsion. Some new existence theorem are obtained and some examples are presented to verify the main results.