Abstract
We consider boundary value problem for nonlinear fractional differential equation D(0+)(alpha)u(t) + f(t,u(t)) = 0, 0 < t < 1, n - 1 < alpha <= n, n > 3, u(0) = u'(1) = u ''(0) = ... = u((0))((n-1)) = 0, where D-0+(alpha) denotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone, and concave.