In this study, the proportional type Newton's law of cooling was discussed, and solutions were obtained on some common time scales. This model, which has a very important place from a physical point of view, was examined in both proportional and delta derivative cases on time scales. Then, the obtained solutions were interpreted graphically, and contributions of time scale calculus with proportional derivative to the theory were revealed. The aim of the study is to examine the effect of the delta and the proportional derivative on the model on time scales.
Çolak et al. (Tue,) studied this question.