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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.