# Lyapunov Inequalities for Nabla Caputo Boundary Value Problems

## TL;DR

This paper develops Lyapunov inequalities for nabla Caputo boundary value problems, providing explicit Green's functions and establishing solution uniqueness for fractional difference equations.

## Contribution

It introduces Lyapunov inequalities for nabla Caputo BVPs and derives explicit Green's functions, advancing fractional difference equation analysis.

## Key findings

- Established uniqueness of solutions for nabla Caputo BVPs
- Derived explicit Green's functions for these problems
- Developed Lyapunov inequalities for specific nabla Caputo BVPs

## Abstract

We will establish uniqueness of solutions to boundary value problems involving the nabla Caputo fractional difference under two-point boundary conditions and give an explicit expression for the Green's functions for these problems. Using the Green's functions for specific cases of these boundary value problems, we will then develop Lyapunov inequalities for certain nabla Caputo BVPs.