On Existence Results for Nonlinear Fractional Differential Equations Involving the p-Laplacian at Resonance

In this paper, we study the existence result for the nonlinear fractional differential equations with p-Laplacian operator where the p-Laplacian operator is defined as denote the Caputo fractional derivatives, and is continuous. Though Chen et al. have studied the same equations in their article, the proof process is not rigorous. We point out the mistakes and give a correct proof of the existence result. The innovation of this article is that we introduce a new definition to weaken the conditions of Arzela-Ascoli theorem and overcome the difficulties of the proof of compactness of the projector K (P) (I - Q)N. As applications, an example is presented to illustrate the main results.