Boundedness and Stability of Solutions of Third Order Nonlinear Vector Neutral Differential Equation with Delay

The main work of this article consists of considering a new class of vector neutral third-order differential equations with multiple delays and investigating three essential qualitative behavior concepts: the uniform asymptotic stability, the boundedness, and the square integrability of solutions for the considered vector neutral third-order differential equation. Three main results are obtained in the form of proven theorems. The method used in the obtention of the main results is the Lyapunov second method, which needs the construction of a new Lyapunov functional that provides this work with the needed conditions to guarantee the main three results. Examples are given to show the reliability of the obtained results.