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Existence of Positive Solutions for Boundary Value Problems with Nonlinear Fractional Differential Equations

~(1,2)Xu Xiaojie ~1Sun Xinguo ~1LüWei (1 School of Mathematics and Computational Science,China University of Petroleum(East China), Shandong Dongying 257061; 2 School of Mathematics and Statistics,Northeast Normal University,Changchun 130024)  
In this paper,the authors consider the properties of Green's function for the nonlinear fractional differential equation boundary-value problem D_(0+)~αu(t)=f(t,u(t)),0t1, u(0)=u(1)=u'(0)=u'(1)=0, where 3α≤4 is a real number,and D_(0+)~αis the standard Riemann-Liouville differentiation, and f:[0,1]×[0.∞)→[0,∞)is continuous.As an application of Green's function,the authors give some multiple positive solutions for nonlinear by means of some fixed-point theorem on cones.
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