Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator

In this article, the author investigates the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator {(D-0+(beta) (phi(p) (D-0+(alpha) u)) (t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) + sigma D-0+(gamma) u(1) = 0, D-0+(alpha) u(0) = 0, where D-0+(beta), D-0+(alpha) and D-0+(gamma) are the standard Riemann-Liouville derivatives with 1 < alpha <= 2, 0 <beta <= 1, 0 <gamma <= 1, 0 <= alpha - gamma - 1, the constant sigma is a positive number and p-Laplacian operator is defined as phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1. By means of the fixed point theorem on cones, some existence and multiplicity results of positive solutions are obtained.