Oscillation for a class of neutral parabolic differential equations

where N is an odd number, Ω is a bounded domain in RM with a smooth boundary ∂Ω, and Δ is the Laplacian operation with three different boundary conditions. We obtained some new oscillatory conditions for the odd-order neutral parabolic differential equation. To some extent, our results are new oscillatory conditions, and extended some oscillatory results of some references.