Application of an Ansatz Method on a Delay Model With a Proportional Delay Parameter

Abstract

Delay differential equations are fundamental tools to modeling various real-world problems. A particular type of these models is considered in this paper in the form y’(t) = ay(t) + aeaty(at), where a is a proportional delay parameter. Solving delay equations is usually a difficult task. This is because there are no standard/well-known methods for solving such kind of equations. This paper proposes a simple procedure to solve the above delay equation. The solution is obtained in closed form which is optimal. The suggested analysis can be invested to analyze more complex models in physics and engineering sciences.