Existence and Uniqueness of Solutions of Nabla Fractional Difference Equations Tending to a Nonnegative Constant

TL;DR

This paper investigates nabla fractional difference equations, providing new conditions for the existence and uniqueness of solutions and analyzing their asymptotic behavior using the Contraction Mapping Theorem.

Contribution

It reformulates previous results on nabla fractional difference equations and establishes comprehensive conditions for solution existence, uniqueness, and asymptotic properties.

Findings

Established conditions for existence of solutions.

Proved uniqueness of solutions under certain conditions.

Analyzed asymptotic behavior of solutions.

Abstract

In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete. By using Contraction Mapping Theorem, we establish conditions under which solutions exist and are unique and have certain asymptotic properties.