Stability Analysis of Higher Order and Fractional Anti-Differences with Mixed Difference Operators

Abstract

The objective of this article is to explore the anti-difference principle using mixed difference operators, deriving theorems for the mth order anti-difference related to finite series. We establish higher order difference equations with factorial coefficients, extending to fractional orders and deriving a fractional anti-difference principle from its integer counterpart. Mixed gamma geometric factorials are introduced to formulate fundamental theorems for mixed fractional difference equations. We analyze the behavior of the th order anti-difference principle, providing a solid theoretical foundation for applying mixed difference operators in discrete dynamics.