# Search Results

## Abstract

In this paper, we study the oscillatory behavior of solutions of the fractional difference equation of the form

where Δ* ^{α}* denotes the Riemann-Liouville fractional difference operator of order

*α*, 0 <

*α*≤ 1, ℕ

_{t0+1−α}={

*t*

_{0}+1−α

*t*

_{0}+2−α…},

*t*

_{0}> 0 and

*γ*> 0 is a quotient of odd positive integers. We establish some oscillatory criteria for the above equation, using the Riccati transformation and Hardy type inequalities. Examples are provided to illustrate the theoretical results.