Stability Results of Solution of Non-Homogeneous Impulsive Retarded Equation Using the Generalized Ordinary Differential Equation

This work is devoted to the study of a non-homogeneous impulsive retarded equation with bounded delays and variable impulse time using the generalized ordinary differential equations (GODEs). The integral solution of the system satisfying the Caratheodory and Lipschitz conditions obtained using the fundamental matrix theorem is embedded in the space of the generalized ordinary differential equations and investigate the problem of stability of the system in the Lyapunov sense. In particular, results on the necessary and sufficient conditions for stability and asymptotic stability of the impulsive retarded system via the generalized ordinary differential equation are obtained. An example is used to illustration the derived theory.