Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator

In this paper, we deal with the following p-Laplacian fractional boundary value problem: phi(p)(D(0+)(alpha)u(t)) + f(t, u(t)) = 0, 0 < t < 1, u(0) = u' (0) = u' (1) = 0, where 2 < alpha <= 3 is a real number. D(0+)(alpha)is the standard Riemann-Liouville differentiation, and f : [0, 1] x [0,+infinity) -> [0,+infinity) is continuous. By the properties of the Green function and some fixed-point theorems on cone, some existence and multiplicity results of positive solutions are obtained. As applications, examples are presented to illustrate the main results.