Existence of the solutions for a class of nonlinear fractional order three-point boundary value problems with resonance

A class of nonlinear fractional order differential equation D(0+)(alpha)u(t) + f (t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) = 1/eta(alpha-1) u(eta) is investigated in this paper, where D-0+(alpha) is the standard Riemann-Liouville fractional derivative of order 1 < alpha <= 2, 0 < eta < 1, f is an element of C([0, 1] x R, R). Using intermediate value theorem, we obtain a sufficient condition for the existence of the solutions for the above fractional order differential equations.