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 intervalD 0 + α u ( t ) + f t , u ( t ) , D 0 + α − 1 u ( t ) = 0 , t ∈ ( 0 , + ∞ ) ,with the integral boundary conditionsu ( 0 ) = 0 ,D 0 + α − 1 u ( ∞ ) = ∫ 0 τg 1 ( s ) u ( s ) d s + a ,D 0 + α − 2 u ( 0 ) = ∫ 0 τg 2 ( s ) u ( s ) d s + b .By using Krasnoselskii fixed point theorem, the existence results of positive solutions for the boundary value problem in three cases τ = 0 , τ ∈ ( 0 , + ∞ ) and τ = + ∞ , are obtained, respectively. We also give out two corollaries as applications of the existence theorems and some examples to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd.