A Study of Deviating Arguments in Existence Differential equations of Solutions | Original Article

ABSTRACT:

Mathematical equations involving derivatives and integrals are used to describe the most fascinating natural phenomenon. In either scenario, these equations are classified as differential or integral equations. Numerous linear and nonlinear differential equations arise in various fields of physical, biological, social, and engineering science. If, when investigating a system, we discover a differential equation, this is referred to as differential equation modeling of the system. Assumption is made that the system and its subsystems interact instantaneously and there is no delay between them in ODE models. Realistic models, on the other hand, incorporate a small bit of lag. As a result, in order to predict the future, it is necessary to take into account the present and the past, as well as derivatives of 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 its present state. The simplest versions of FDEs are known as delay differential equations (DDE). For this reason, they are known as differential equations with a retarded argument, or DARs for short. When the unknown function at the delayed argument takes a derivative, we have a neutral delay differential equation (NDDE).