Model of economic growth in the context of fractional derivative

Abstract

The objective of this paper is to revisit one economic model in the context of the fractional calculus. The considered considered is the economic growth model in the context of the Caputo-Liouville derivative. The problem consists of determining the optimal growth rate value by maximizing in infinite time the utility function of the total consumption of firms. In other words, we consider the Ramsey model represented by the fractional Caputo-Liouville derivative. The optimization procedure uses the Hamiltonian function. The solutions obtained from the proposed model are graphically represented and interpreted using mathematical and economic backgrounds. We also analyze the consumption and the capital in term of Mittag–Leffler’s input stability.

Keywords

• Fractional calculus
• Fractional derivatives
• Economic growth model
• Utility function