Representation and Stability of Solutions for Systems of Delay Difffferential Equations With Multiple Constant Delays

Abstract

Delay differential equation is type functional differential equations that arise in numerous areas of applied sciences. Various forms of these equations play a vital role in mathematical modelling of real-life phenomena.Different techniques have been use to obtain solutions of various types of delay differential equations (DDEs). However, many situations arising in the theory of DDEs in which the solution of certain types of nonlinear DDEs cannot be explicitly obtained. In such a case, having a suitable representation for the solutions, some important properties such as oscillation and stability of these equations can be obtained. Therefore, in this work, a Natural transform and convolution theorem are used to derive a closed form-formula for the representation of solution for nonlinear systems of DDEs. The derived result is also used to study the exponential stability for the solution of nonlinear systems of DDEs. Hence, the approach can also be applied to study the stability analysis of many types of nonlinear problems.