EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO HIGHER-ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH INTEGRAL BOUNDARY CONDITIONS

In this article, we consider the nonlinear fractional order three-point boundary-value problem D-0+(alpha) u(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = u' (0) = center dot center dot center dot = u((n-2))(0) = 0, u((n-2))(1) = integral(n)(0) u(s) ds, where D-0+(alpha) is the standard Riemann-Liouville fractional derivative, n - 1 < alpha <= n, n >= 3. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions to the above boundary value problem.