In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.

This paper investigates the anti-periodic boundary value problem for multi-term fractional differential equations that involve the $p$-Laplacian operator. We establish existence results by separately applying the Leray-Schauder nonlinear alternative and the Krasnosel'skii's fixed point theorem. Finally, two illustrative examples are presented to demonstrate the effectiveness of the main results.

This paper investigates the existence and uniqueness of solutions for several two-point fractional BVPs, including hybrid fractional BVP, sequential fractional BVP and so on. Using the Banach contraction mapping theorem, some sharp conditions that depend on the length of the given interval are presented, which ensure the uniqueness of solutions for the considered BVPs. Illustrative examples are also constructed. The results obtained in this study are noteworthy extensions of earlier works.

In this paper, we investigated a class of nonlinear triply coupled systems of fractional Langevin equations subject to closed boundary conditions. The existence of solutions to the proposed boundary value problem was first established by applying Krasnoselskii's fixed point theorem. Furthermore, the uniqueness of the solution was obtained via the Banach contraction mapping principle. To demonstrate the effectiveness of the theoretical results, illustrative examples are provided.