# Lyapunov inequality for a boundary value problem involving conformable derivative

## TL;DR

This paper investigates a boundary value problem with conformable derivatives of order between 1 and 2, establishing existence of solutions using fixed-point methods and deriving a Lyapunov inequality for the problem.

## Contribution

It introduces a Lyapunov inequality for boundary value problems involving conformable derivatives, expanding analytical tools for fractional differential equations.

## Key findings

- Existence of solutions proven using upper and lower solutions and Schauder's fixed-point theorem.
- Derived a Lyapunov inequality specific to conformable derivative boundary value problems.
- Provides theoretical foundation for stability analysis of such fractional differential equations.

## Abstract

We consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's fixed-point theorem. \ Futhermore, we give the Lyapunov inequality for the corresponding problem.