Analytical Solutions for Advanced Functional Differential Equations with Discontinuous Forcing Terms and Studying Their Dynamical Properties

Abstract

This paper aims to find new analytical closed-forms to the solutions of the nonhomogeneous functionaldifferential equations of the nth order with finite and constants delays and various initial delay conditions interms of elementary functions using Laplace transform method. As well as, the definition of dynamicalsystems for ordinary differential equations is used to introduce the definition of dynamical systems for delaydifferential equations which contain multiple delays with a discussion of their dynamical properties: Theexponential stability and strong stability