Existence of positive solutions for integral boundary value problems of fractional differential equations on infinite interval

In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval D(0+)(alpha)u(t) + f (t,u(t), D(0+)(alpha=1)u(t)) = 0, t is an element of(0, +infinity), with the integral boundary conditions u(0) = 0, D(0+)(alpha-1)u(infinity) = integral(tau)(0) g(1)(s)u(s)ds + a, D(0+)(alpha-2)u(0) = integral(tau)(0) g(2)(s)u(s)ds + b. By using Krasnoselskii fixed point theorem, the existence results of positive solutions for the boundary value problem in three cases tau = 0, tau is an element of(0, +infinity) and tau = +infinity, are obtained, respectively. We also give out two corollaries as applications of the existence theorems and some examples to illustrate our results. Copyright (C) 2016 John Wiley & Sons, Ltd.