## A differential equation is said to be an integro-differential equation (IDE) if it contains the integrals of the unknown function. When the current state of such an integro-differential equation now depends on the previous states, it is known to be a time-delay integro-differential equation. Indeed, it is a well-known fact that stability and boundedness properties of solutions of second order (also higher order) ordinary differential equations and integro-differential equations with or without delay have many applications in many fields of science and technology such as biology, medicine, engineering, informa- tion system, control theory and financial mathematics. Therefore, the study of their qualitative properties has attracted the attention of many researchers, see (  - ) and references contained in them. Readers are referred to  for an exposi- tory treatment of Volterra integral and differential equations. A differential equation is said to be an integro-differential equation (IDE) if it
contains the integrals of the unknown function. When the current state of such an
integro-differential equation now depends on the previous states, it is known to be
a time-delay integro-differential equation.
Indeed, it is a well-known fact that stability and boundedness properties of
solutions of second order (also higher order) ordinary differential equations and
integro-differential equations with or without delay have many applications in many
fields of science and technology such as biology, medicine, engineering, informa-
tion system, control theory and financial mathematics. Therefore, the study of
their qualitative properties has attracted the attention of many researchers, see ( 
- ) and references contained in them. Readers are referred to  for an exposi-
tory treatment of Volterra integral and differential equations.       