On the Oscillation of Nonlinear Fractional Difference Equations

M. Reni Sagayaraj, A.George Ma

Abstract

In this paper, we study oscillatory behavior of the fractional difference equations of the following form ∆ (p(t)(∆αx(t))γ )+q(t)f t−X 1+α s=t0 (t − s − 1)(−α)x(s) ! = 0, t ∈ Nt0+1−α, where ∆α denotes the Riemann-Liouville difference operator of order α, 0 < α ≤ 1 and γ > 0 is a quotient of odd positive integers. We establish some oscillation criteria for the above equation by using Riccati transformation technique and some Hardy type inequalities. An example is provided to illustrate our main results.