Comparison criteria for odd order forced nonlinear functional neutral dynamic equations

The purpose of this paper is to establish comparison criteria for forced odd order neutral dynamic equation[x(t)+p(t)x(τ(t))][n]+q(t)ϕγ(x(φ(t)))=g(t),x(t)+p(t)x(τ(t))n+qtϕγxφt=g(t),on an above-unbounded time scale TT, where n⩾3;ϕγ(u)≔uγ-1u,γ>0;p,q∈Crdt0,∞T,R+ on t0,∞T;g∈Crd([t0,∞)T,R); and τ,φ:T→T are rd-continuous functions such that limt→∞τ(t)=limt→∞φ(t)=∞limt→∞τ(t)=limt→∞φ(t)=∞. Comparison criteria have been established without assuming certain restrictive conditions on the time scale TT which improve some results in a number of recent papers.