A Remark on the Memory Property of Fractional Difference Operators

TL;DR

This paper examines how the nonlocal memory property of fractional difference operators influences the long-term behavior of solutions to nabla fractional difference equations, highlighting its impact on qualitative analysis.

Contribution

It provides insights into the effect of the memory property on the asymptotic behavior of solutions, advancing understanding of fractional difference equations.

Findings

Memory property affects asymptotic solutions

Nonlocal structure complicates qualitative analysis

Results enhance understanding of fractional difference equations

Abstract

Fractional difference operators possess nonlocal structure which largely affects and complicates the qualitative analysis of fractional difference equations. In this article, we discuss the effect of this memory property on asymptotic behaviour of solutions of nabla fractional difference equations.