# Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities

## TL;DR

This paper establishes the existence of positive solutions for a discrete fractional boundary value problem and derives related Lyapunov-type inequalities, expanding the understanding of fractional difference equations.

## Contribution

It introduces new existence results for positive solutions and formulates Lyapunov-type inequalities specific to discrete fractional boundary value problems.

## Key findings

- Positive solutions are proven to exist for the considered boundary value problem.
- New Lyapunov-type inequalities are derived for discrete fractional operators.
- The results extend classical inequalities to the fractional discrete setting.

## Abstract

We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.