New qualitative results to a kind of non-autonomous third-order neutral delay differential equations

In this paper, the qualitative properties of solutions for a kind of nonautonomous third-order neutral delay differential equations (NDDEs) are discussed. New results on the stability, bounderness and square integrability of solutions and their derivatives are obtained by using the method of Layapunov functional. Our results generalize and extend many related results on third order neural differential equations with and without delay in the literature. Moreover, an example is given to show the correctness and feasibility of the main results. In this paper, the Lyapunov functional approach is applied to investigate a third-order non-autonomous neutral delay differential equation. To ensure the stability, bounderness, and square integrability of solutions, the standard Lyapunov functional is designed to fulfill the necessary requirements. Our findings add to the body of excellent existing research in the literature and make several new discoveries. To exemplify the efficacy of the achieved results, an example was suggested that performed the supplied results in all functions.