In this paper, new sufficient conditions are established for the oscillation of solutions of the higher order dynamic equations [r(t)(z ∆n−1 (t)) α] ∆ + q(t) f (x(δ(t))) = 0, for t ∈ [t 0 , ∞) T , where z(t) := x(t) + p(t)x(τ(t)), n ≥ 2 is an even integer and α ≥ 1 is a quotient of odd positive integers. Under less restrictive assumptions for the neutral coefficient, we employ new comparison theorems and Generalized Riccati technique.