Existence and Uniqueness of Solution for Fractional Differential Equations with Integral Boundary Conditions

This paper is devoted to the existence and uniqueness results of solutions for fractional differential equations with integral boundary conditions. {(C)D(alpha)x(t) + f(t, x(t), x'(t)) = 0, t is an element of (0, 1), x(0) = integral(1)(0) g(0)(s, x(s))ds, x(1) = integral(1)(0) g(1)(s, x(s))ds, x((k)) (0) = 0, k = 2, 3, ..., [alpha] - 1. By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order alpha.