The main goal of this paper is to use non-local fractional operators, specifically the generalized proportional fractional Caputo derivatives, to analyze certain economic problems. The paper also compares the results obtained using these fractional operators with already established results using many other different kinds of the fractional derivatives. At the end, a more comprehensive view of considered economic problems in the market, which includes simulation analysis, is provided.
In the realm of the generalized proportional Caputo fractional derivative, we encounter the most comprehensive scenario. With adjustments to the parameters $\xi$ and $g(t)$, the solution graphs can closely resemble those obtained from employing other types of fractional derivatives. This flexibility allows for a wide range of modeling possibilities and facilitates the comparison and analysis of various economic systems.
By leveraging the generalized proportional Caputo fractional derivative, researchers can explore the dynamics of economic models in a more versatile manner. This approach enables us to capture different aspects of economic behavior and investigate the impacts of varying parameters on the system's dynamics. The ability to closely approximate solutions obtained from other fractional derivatives provides a valuable tool for understanding the interconnectedness and similarities among different economic phenomena.