In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundaryvalue problem D α u(t) = f (t, u(t)) with a RiemannLiouville fractional derivative via the different boundary-value problems u(0) = u(T), and the threepoint boundary condition u(0) = β 1 u(η) and u(T) = β 2 u(η), where T > 0, t ∈ I = [0, T], 0 < α < 1, 0 < η < T, 0 < β 1 < β 2 < 1.