Two-Point Boundary Value Problems for Fractional Differential Equations at Resonance

In this paper, by using the coincidence degree theory, we consider the following two-point boundary value problem for fractional differential equation ( D a+ x(t) = f(t; x(t); x 0 (t)); t2 (0; 1); x(0) = 0; x 0 (0) = x 0 (1); where D a+ denotes the Caputo fractional differential operator of order a, 1 < a 2. A new result on the existence of solutions for above fractional boundary value problem is obtained.