Uniqueness and Stability of Solutions for a Coupled System of Nabla Fractional Difference Boundary Value Problems

TL;DR

This paper establishes conditions for the existence, uniqueness, and stability of solutions to a coupled system of nabla fractional difference boundary value problems, using fixed point theorems and providing an illustrative example.

Contribution

It introduces new sufficient conditions for solution existence, uniqueness, and stability specifically for coupled nabla fractional difference boundary value problems.

Findings

Conditions for existence and uniqueness are derived.

Ulam-Hyers stability of solutions is established.

An example demonstrates the applicability of the results.

Abstract

In this article, we obtain sufficient conditions on existence, uniqueness and Ulam--Hyers stability of solutions for a coupled system of two-point nabla fractional difference boundary value problems, using Banach fixed point theorem and Urs's approach. Finally, we illustrate the applicability of established results through an example.