We present here a new type of three-point nonlinear fractional boundary value problem of arbitrary order of the form cDq u(t) = f(t, u(t)), t ∈ [0, 1], u(η) = u′ (0) = u′′ (0) = · · · = un −2(0) = 0, Ipu(1) = 0, 0 < η < 1, where n − 1 < q ≤ n, n ∈ N, n ≥ 3 andcDq denotes the Caputo fractional derivative of order q, Ip is the Riemann-Liouville fractional integral of order p, f: [0, 1] × R → R is a continuous function and ηn−1 (Equation presented). We give new existence and uniqueness results using Banach contraction principle, Krasnoselskii, Scheafer’s fixed point theorem and Leray-Schauder degree theory. To justify the results, we give some illustrative examples. © 2018, Drustvo Matematicara Srbije. All rights reserved.