Second order neutral multi-delay differential equations and its oscillatory criteria derived by linearization

In this paper, we investigate the oscillatory behavior of second-order neutral multi-delay differential equations$ \begin{equation*} \left( r \left({t}\right)\left[\left( u\left({t}\right) + \sum\limits_{i = 1}^nb_i(t)u(\psi_i(t))\right)'\right]^{\alpha}\right)^\prime + Q\left({t}, u\left( \tau \left({t}\right)\right)\right) = 0. \end{equation*} $We introduce new monotonic properties of the non-oscillatory solutions of the equation, which are then used to linearize the equation and derive new oscillatory criteria. Our results are further supported by a numerical simulation example.