Asymptotic Stability of Two Classes of Second Order Nonlinear Neutral Delay Differential Equations with Variable Delays

Extensions of two well known existing results for solutions of second order nonlinear neutral delay differential equations with variable delay by modifying some constraint conditions are considered in this study. A new method is developed for the solutions of the modified equations considering fixed point approach with two auxiliary functions on a contraction condition. It is found that new criteria for asymptotic stability are established and some stability properties of the modified equations are also obtained.