Existence on positive solutions for boundary value problems of nonlinear fractional differential equations with p-Laplacian

In this paper, we study the existence of positive solutions for the nonlinear fractional boundary value problem with a p-Laplacian operator D-0+(beta)(phi p((D0+U)-U-alpha(t))) = f(t, u(t)), 0 < t < 1, u(0) = u'(0) = u'(1) = 0, D(0+)(alpha)u(0) = D(0+)(alpha)u(1) = 0 where 2 < alpha <= 3, 1 < beta <= 2, D-0+(alpha), D-0+(beta) are the standard Riemann-Liouville fractional derivatives, phi(p)(s) = vertical bar s vertical bar(p-2) s, p > 1, phi(-1)(p) = phi(q), 1/p + 1/q = 1 and f(t, u) is an element of C([0, 1] x [0, +infinity), [0, +infinity)). By the properties of Green's function, the Guo-Krasnosel'skii fixed-point theorem, the Leggett-Williams fixed-point theorem, and the upper and lower solutions method, some new results on the existence of positive solutions are obtained. As applications, examples are presented to illustrate the main results.