Positive Solution for the Nonlinear Hadamard Type Fractional Differential Equation with p-Laplacian - Ya-ling Li; Shi-you Lin (Journal of Function Spaces and Applications)
We study the following nonlinear fractional differential equation involving the p-Laplacian operator DβφpDαut=ft,ut, 1<t<e, u1=u′1=u′e=0, Dαu1=Dαue=0, where the continuous function f:1,e×0,+∞→[0,+∞), 2<α≤3, 1<β≤2. 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.