Positive solutions for an impulsive boundary value problem with Caputo fractional derivative

In this work we use fixed point theorem method to discuss the existence of positive solutions for the impulsive boundary value problem with Caputo fractional derivative {(c) D(t)(q)u(t) = f (t,u(t)), a.e. t is an element of [0,1]; Du(t(k)) = I-k(u(t(k))), Delta u'(t(k)) = J(k)(u(t(k))), k = 1, 2,..., m; au(0) - bu(1) = 0, au'(0) - bu'(l) = 0, where q is an element of (1, 2) is a real number, a, b are real constants with a > b > 0, and (c) D-t(q) is the Caputo's fractional derivative of order q, f : [0,1] x R+ -> R+ and I-k, J(k) : R+ -> R+ are continuous functions, k = 1,2,..., m, R+ := [0, + infinity). (C) 2016 All rights reserved.