Positive properties of the Green function for twoterm fractional differential equations and its application

In this paper, we study the positive properties of the Green function for the following twoterm fractional differential equation -D^α0 + u(t)=f(t,u(t)), 0 t 1, u(0)=0 , u(1)=0 where 1 α 2, b 0, D^α0 is the standard RiemannLiouville derivative. As an application, the existence and uniqueness of positive solution are obtained under the singular conditions. Moreover, an iterative scheme is established to approximate the unique positive solution.