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The aim of this paper is to give oscillation criteria for the third-order neutral dynamic equations with distributed deviating arguments of the form \begin { equation* } \bigg [r(t) \big ([x(t)+p(t)x( \tau (t))]^{ \Delta\Delta } \big )^{ \gamma } \bigg ]^{ \Delta }+ \int_ {c}^{d}f(t,x[ \phi (t, \xi )]) \Delta\xi=0, \end { equation* } where $\gamma>0$ is the quotient of odd positive integers with $r$ and $p$ real-valued rd -continuous positive functions defined on $\mathbb{T}$ . $\phi(t,\xi)\in C_{rd}([t_{0},\infty)\times[c,d],\mathbb{T})$ is not decreasing function for $\xi$ and such that $\phi(t,\xi)\leq t$ and $\lim_{t\rightarrow\infty}\min_{\xi\in[c,d]}\phi(t,\xi)=\infty$ . We establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.

Oscillation behavior of third-order nonlinear neutral dynamic equations on time scales with distributed deviating arguments