LYAPUNOV-TYPE INEQUALITY FOR BOUNDARY VALUE PROBLEMS WITH HADAMARD FRACTIONAL DERIVATIVES AND APPLICATIONS

By Nguyen Dinh Duong
DOI: 10.37550/tdmu.EJS/2025.04.692

In this paper, we consider a boundary value problem involving the Hadamard fractional derivative. We establish a Lyapunov-type inequality for the problem by constructing the green function and analyzing its properties. Next, we employ a fixed-point theorem to obtain the existence and uniqueness of the solution to the problem. The paper concludes with three examples that illustrate the theoretical results.