A generalized Lyapunov's inequality for a fractional boundary value problem

TL;DR

This paper establishes the existence of positive solutions for a nonlinear fractional boundary value problem and introduces a generalized Lyapunov's inequality under mild nonlinear assumptions, supported by illustrative examples.

Contribution

It provides a novel generalization of Lyapunov's inequality tailored for fractional boundary value problems, expanding theoretical tools in this area.

Findings

Existence of positive solutions demonstrated.

A generalized Lyapunov's inequality proved.

Examples illustrating the new results included.

Abstract

We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated through examples.