A Study of Deviating Arguments in Differential- Difference Equations of Order | Original Article

ABSTRACT:

Ordinary differential equations (ODEs) are frequently employed in modeling research. If a system is modelled using ordinary differential equations (ODEs), we presume that the current state has no influence over what will happen in the future. 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 this study, of the FDEs has developed considerably in past few decades, the reason being its wide application in physical and biological system. System inheritance is taken into account in both physical and biological model systems. The examples and applications of differential equations with diverging arguments have piqued my interest in studying them further. Many different types of problems can be solved using differential equations with diverging arguments. The findings of this study should be examined further According to what has been said, there appears to be plenty of room to analyze these equations in terms of properties such as asymptotic behavior, periodicity, anti-periodicity, stability, and so on. There hasn't been enough discussion of boundary value limitations. Nonlinear systems' Observability and controllability can be investigated.