New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution

In this paper, we consider the second-order nonlinear neutral functional dynamic equation(p(t)([y(t) + r(t)y(tau(t))](Delta))(gamma))(Delta) + f(t,y(delta(t))) = 0,on a time scale T and establish some new sufficient conditions for oscillation. Our results improve oscillation results for neutral delay dynamic equations on time scales and are new when delta(t) t and or 0 gamma 1. Furthermore our results can be applied on the time scales T = hT, for h 0, T = q(N) = {t : t = q(k)}, k is an element of N, q 1, T = N-2 = {t(2) : t is an element of N}, T-2 = {root n : n is an element of N-0}, T3 = {(3)root n : n is an element of N-0}, and when T = Tn = {t(n) : n is an element of N-0} where {tn} is the set of harmonic numbers, etc.