A Study of Deviating Arguments in Existence Differential equations of Solutions

Incorporating Lag and Delay: Modeling Systems with Deviating Arguments

Abstract

Mathematical equations involving derivatives and integrals are used to describe the mostfascinating natural phenomenon. In either scenario, these equations are classified as differential orintegral equations. Numerous linear and nonlinear differential equations arise in various fields ofphysical, biological, social, and engineering science. If, when investigating a system, we discover adifferential equation, this is referred to as differential equation modeling of the system. Assumption ismade that the system and its subsystems interact instantaneously and there is no delay between themin ODE models. Realistic models, on the other hand, incorporate a small bit of lag. As a result, in orderto predict the future, it is necessary to take into account the present and the past, as well as derivativesof the former. Functional differential equations are used to model these models (FDEs). In many cases,FDEs are preferable than ODEs because of the implicit assumption that the system's past influences itspresent state. The simplest versions of FDEs are known as delay differential equations (DDE). For thisreason, they are known as differential equations with a retarded argument, or DARs for short. When theunknown function at the delayed argument takes a derivative, we have a neutral delay differentialequation (NDDE).