Economic models including proportional derivative on time scales

This thesis examines the application of time scale theory to supply and demand models, interest rate models, and inflation forecasting models in economics using proportional derivatives. The first part of the thesis conducts a comprehensive literature review on the concepts of time scales and proportional derivatives on time scales. This literature review aims to provide the theoretical basis for how these concepts can be used in economic modeling. In the second part of the study, supply and demand, compound interest, and inflation forecasting models are analyzed using classical analysis methods, and the solutions of these models are examined in detail. In the following sections, supply and demand, interest rate, and inflation forecasting models are reconstructed using time scale theory and proportional derivatives. Within this framework, the concept of proportional derivatives is integrated into economic models, and solutions for these extended models are obtained. Furthermore, the theoretical results are supported by numerical examples, demonstrating the applicability of the models. This study demonstrates that the integration of time scale theory and proportional derivatives into economic modeling provides a more flexible and extensible framework compared to classical analysis methods.