On positive solutions for am-point fractional boundary value problem on an infinite interval

In this paper, by using a recent fixed point theorem, we study the existence and uniqueness of positive solutions for the following m-point fractional boundary value problem on an infinite interval Da 0+ x(t) + f (t, x(t)) = 0, 0 < t < 8, x(0) = x (0) = 0, Da-1 0+ x(+8) = m-2 i= 1 beta i x(.i), where 2 < a < 3, Da 0+ is the standard Riemann- Liouville fractional derivative, Da-1 0+ x(+8) = lim t.8 Da-1 0+ x( t), 0 <.1 <.2 < center dot center dot center dot <.m- 2 < 8 and beta i = 0 f or i = 1, 2,..., m - 2. Moreover, we present an example illustrating our results.