# Lyapunov-type inequality for a fractional boundary value problem with natural conditions

## TL;DR

This paper establishes a new Lyapunov-type inequality for fractional boundary value problems involving Riemann-Liouville and Caputo derivatives, with applications to eigenvalue problems.

## Contribution

It introduces a novel Lyapunov inequality for fractional derivatives with natural boundary conditions, extending previous results in fractional calculus.

## Key findings

- Derived a new Lyapunov inequality for fractional boundary value problems.
- Applied the inequality to analyze eigenvalue problems in fractional calculus.
- Extended classical inequalities to fractional derivatives with natural conditions.

## Abstract

We derive a new Lyapunov type inequality for a boundary value problem involving both left Riemann--Liouville and right Caputo fractional derivatives in presence of natural conditions. Application to the corresponding eigenvalue problem is also discussed.