Investigating Differential Difference Equations: An In-Depth Review

Investigating Differential Difference Equations: An In-Depth Review

Differential difference equations serve as mathematical models for a wide range of physical phenomena. Differential difference equations have a broad spectrum of applications spanning various disciplines. These equations find diverse applications in a wide range of fields, including epidemiology, information technology, control theory, finance, population dynamics, and stochastic processes. Their adaptability in modeling systems characterized by a blend of continuous and discrete behaviors renders them an invaluable mathematical framework with applicability spanning numerous domains in science and engineering. This study provides a comprehensive review of existing literature pertaining to periodic solutions, entire solutions, asymptotic analysis, and numerical approaches for differential difference equations. The pri- mary objective of this research is to analyze the various problems and methodologies employed in the extant literature. Notably, significant advancements in this field have been made since 1946. As a result, this study aims to encompass the research conducted by various scholars from 1946 to 2023.