Oscillation of solutions for a class of nonlinear fractional difference equations

In this paper, we investigate the oscillation of the following nonlinear fractional difference equations, \[\Delta(a (t) [\Delta(r (t) (\Delta^\alpha x (t))^{\gamma_1} )] ^{\gamma_2}) + q (t) f (\Sigma^{t1+\alpha}_{s=t_0} (t s 1)^{(\alpha)} x (s) )= 0,\] where \(t \in N_{t_0+1\alpha},\gamma_1\) and \(\gamma_2\) are the quotient of two odd positive number, and \(\Delta^\alpha\) denotes the Riemann Liouville fractional difference operator of order \(0 \alpha\leq 1\).