In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equationswhere λ, µ, ν are three parameters with 0 < µ < β and 0 < ν < α, α, β ∈ (n − 1, n] are two real numbers and n ≥ 3, D α , D β are the Hadamard fractional derivative of fractional order, and f, g are sign-changing continuous functions and may be singular at t = 1 or/and t = e. First of all, we obtain the corresponding Green's function for the boundary value problem and some of its properties. Furthermore, by means of the nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorems, we derive an interval of λ such that the semipositone boundary value problem has one or multiple positive solutions for any λ lying in this interval. At last, several illustrative examples were given to illustrate the main results. c 2015 All rights reserved.

This paper investigates a class of nonlinear p-Laplacian Hadamard fractional differential systems with coupled nonlocal Riemann-Stieltjes integral boundary conditions. First, we obtain the corresponding Green?s function for the considered boundary value problems and some of its properties. Then, by using the Guo-Krasnosel?skii fixed point theorem, some sufficient conditions for existence and nonexistence of positive solutions for the addressed systems are obtained under the different intervals of the parameters ? and ?. As applications, some examples are presented to show the effectiveness of the main results.