Investigation of Newton's Law of Cooling on Time Scales with Proportional Derivative

In this study, the proportional type Newton’s law of cooling is discussed, and solutions are obtained on some common time scales. This model, which plays an important role in physics, is examined in both proportional and delta derivative cases on time scales. Then, the obtained solutions are interpreted graphically, and the contributions of time scale calculus with proportional derivative to the theory are revealed. The aim of the study is to examine the effect of the delta and the proportional derivative on the model on time scales.