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In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transformation technique, we employ herein an easily verifiable approach based on the fractional Taylor's difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.

Abstract In this paper, we consider the oscillation behavior of solutions of the following fractional difference equation: Δ(c(t)Δ(a(t)Δ(r(t)Δαx(t))))+q(t)G(t)=0, $$ \Delta \bigl( c ( t ) \Delta \bigl( a ( t ) \Delta \bigl( r ( t ) \Delta^{\alpha }x ( t ) \bigr) \bigr) \bigr) +q ( t ) G ( t ) =0, $$ where t∈Nt0+1−α $t\in \mathbf{N}_{t_{0}+1-\alpha }$, G(t)=∑s=t0t−1+α(t−s−1)−αx(s) $G ( t ) = \sum_{s=t_{0}}^{t-1+\alpha } ( t-s-1 ) ^{-\alpha }x ( s ) $, and Δα $\Delta^{\alpha }$ denotes a Riemann–Liouville fractional difference operator of order 0

Abstract In this study, we discuss some theorems related to the oscillatory behavior of nonlinear fractional difference equations equipped with well-known fractional Riemann–Liouville difference operator. Then we give an example for the illustration of the results obtained.

In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.