Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model

TL;DR

This paper introduces a novel mathematical approach using the Katugampola generalized conformal derivative to extend the Solow-Swan economic growth model, impacting convergence speed and adding a new interpretable parameter.

Contribution

It extends the Solow-Swan model with a new derivative-based parameter, providing insights into convergence behavior without adding new state variables.

Findings

The order of KGCD affects convergence speed of solutions.

The model's new parameter has meaningful economic interpretations.

Extensions of Inada conditions depend on KGCD order.

Abstract

This article shows a new focus of mathematic analysis for the Solow-Swan economic growth model, using the generalized conformal derivative Katugampola (KGCD). For this, under the same Solow-Swan model assumptions, the Inada conditions are extended, which, for the new model shown here, depending on the order of the KGCD. This order plays an important role in the speed of convergence of the closed solutions obtained with this derivative for capital (k) and for per-capita production (y) in the cases without migration and with negative migration. Our approach to the model with the KGCD adds a new parameter to the Solow-Swan model, the order of the KGCD and not a new state variable. In addition, we propose several possible economic interpretations for that parameter.