Combining the properties of the Green function with some point theorems, we consider the existence of nontrivial solutions for fractional equations with p-Laplacian operator D0+βϕp[D0+α(ptu′(t))]+f(t,u(t))=0, 0<t<1, au(0)-bp0u′(0)=0, and cu(1)+dp1u′(1)=0, D0+αptu′tt=0=0, where a,b,c,d are constants and p(·):[0,1]→(0,+∞) is continuous.

In this paper, we establish several new existence theorems for positive solutions of systems of \((2n,2m)\)-order of two p-Laplacian equations. The results are based on the Krasnosel’skii fixed point theorem and mainly complement those of Djebali, Moussaoui, and Precup.

We mainly consider the existence and stability results of the positive solutions for the fractional differential equation with Hadamard-type by applying fixed point theorems, if the nonlinearity may be continuous or singular. We also construct some examples to show the applicability of the results.