A brief overview of the stability theory of integro-differential equations

In this chapter an overview of the theory of Lyapunov stability of integro-differential equations (InDEs) is presented. The chapter is divided into two parts. In the first part the stability theory of different types of linear InDEs is discussed and different approaches to study stability concepts are given. The second part covers the stability theory of nonlinear Volterra InDEs using the comparison method. Various types of stability notions, such as, practical stability and stability in terms of two measures are some of the topics discussed.