Existence of Solutions for a Coupled System of p-Laplacian Caputo–Hadamard Fractional Sturm–Liouville–Langevin Equations with Antiperiodic Boundary Conditions

Abstract

Fractional Sturm–Liouville and Langevin equations have recently attracted much attention. In this paper, we investigate a coupled system of fractional Sturm–Liouville–Langevin equations with antiperiodic boundary conditions in the framework of Caputo–Hadamard fractional derivative. Comparing with the existing literature, we study fractional differential equations with a p-Laplacian operator, which will enrich and generalize the previous work. Based on the Leray–Schauder nonlinear alternative and Krasnoselskii’s fixed point theorem, some interesting existence results are obtained. Finally, an example is constructed to illustrate our main results.