Armament model and its analysis with proportional derivative on time scales

In this study, we address the Richardson arms race model, a analyze the dynamics of military competition between two or more this model is to investigate how the defense expenditures of states to determine whether such interactions lead to a stable equilibrium or We will explore this model through both classical analysis and a comprehensive examination of its theoretical and applied attitudes of countries towards each other by presenting information on to support these analyses with examples. In solving the proportional we will employ the proportional Laplace transform on time scales and dynamic equations in proportional time scales.