Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian

Abstract EN

We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut, 1

Dα denotes the standard Hadamard fractional derivative of the order α, the constant p>1, and the p-Laplacian operator φps=sp-2s.

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.