In this paper, we study the existence of a solution for the nonlinear implicit fractional differential equation of the type D α u(t) = f (t, u(t), D α u(t)) , with Riemann-Liouville fractional derivative via the different boundary conditions u(0) = u(T), and the three point boundary conditions 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