Positive solution for the nonlinear Hadamard type fractional differential equation with p-Laplacian

We study the following nonlinear fractional differential equation involving the p -laplacian operator d β p d α u t = f t,u t,1 < t < e,u 1 = u ′ 1 = u ′ e = 0,d α u 1 = d α u e = 0,where the continuous function f: 1,e × 0,+ ∞ → [ 0,+ ∞),2 < α ≤ 3,1 < β ≤ 2. d α denotes the standard hadamard fractional derivative of the order α,the constant p > 1,and the p -laplacian operator p s = s p - 2 s. we show some results about the existence and the uniqueness of the positive solution by using fixed point theorems and the properties of green's function and the p -laplacian operator. © 2013 ya-ling li and shi-you lin.