Existence and Uniqueness of Solutions for Singular Fractional Integro-Differential Equations with p-Laplacian and Two Kinds of Fractional Derivatives

The paper is devoted to the study of a class of singular high-order fractional integro-differential equations with p-Laplacian operator, involving both the Riemann–Liouville fractional derivative and the Caputo fractional derivative. First, we investigate the problem by the method of reducing the order of fractional derivative. Then, by using the Schauder fixed point theorem, the existence of solutions is proved. The upper and lower bounds for the unique solution of the problem are established under various conditions by employing the Banach contraction mapping principle. Furthermore, four numerical examples are presented to illustrate the applications of our main results.