In this paper, we introduce a new class of boundary value problems consisting of a fractional differential equation of Riemann-Liouville type, D q R L x(t)=f(t,x(t)), t∈[0,T], subject to the Hadamard fractional integral conditions x(0)=0, x(T)= ∑ i = 1 n α i H I p i x( η i ). Existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples illustrating the results obtained are also presented.MSC: 34A08, 34B15.