Discrete and Continuous Fractional Economic Models Based on Market Equilibrium in the Frame of Different Type

Abstract

In this thesis we investigate the solutions of continuous and discrete fractional economic models using the non-local discrete fractional differences and derivatives involving Caputo, Caputo – Fabrizio in the sense of Caputo (CFC), Caputo type Atangana – Baleanu (ABC) and ABC with generalized Mittag Leffler kernel. These differences and derivatives and fractional factors enable us to solve with equations more generally, as they go beyond dealing with integrals and regular derivatives and enable us to deal with more complex equations and tolerate wider mathematical explanations. In the case of the economic models that we are dealing with, these differences enable us to better understand the market body and the relationship between xi supply and demand and their interactions with the price adjustment on the assumption that the market is in equilibrium. The main original part is to solve and investigate the economic models by using the discrete counter part of the above, Caputo type for final operators in the power low, exponantial nabla low, nabla Mittag-Leffler low and generalized nabla Mittag-Leffler low and solve the models in the continuous case analytically. Our research is unique because we review the solutions of these models in the discrete case, in addition to that we are the first to review Generalized ABC with four parameters and the dependence of the rest of the differences on them as special cases. Finally, we interpret the results we obtain from the model and compare them in more details with the different solutions we obtain. [1–41