Analysis of Solow-Swan model with nonlocal fractional derivative operator

TL;DR

This paper extends the classical Solow-Swan economic growth model by incorporating fractional derivatives to better capture memory effects in capital accumulation, providing a more comprehensive understanding of macroeconomic dynamics.

Contribution

It introduces a fractional calculus-based extension to the Solow-Swan model, highlighting the impact of memory effects on economic growth analysis.

Findings

Fractional model captures memory effects in capital dynamics.

Comparison shows differences between classical and fractional models.

Enhanced understanding of long-term economic behavior.

Abstract

The Solow-Swan equation is a foundational model in the evolution of modern economic growth theory. It offers key insights into the long-term behaviour of capital accumulation and output. Since its inception, the model has served as a cornerstone for understanding macroeconomic dynamics and has inspired a vast body of subsequent research. However, traditional formulations of the Solow-Swan model rely on integer-order derivatives, which may not fully capture the memory and hereditary properties often observed in real-world economic systems. In this paper, we extend the classical Solow-Swan framework by incorporating memory effects through the use of fractional calculus. The fractional model accounts for the influence of past states on the present rate of capital change, a feature not accommodated in the standard model. We present a comparative analysis of the capital dynamics under both the classical and fractional-order formulations of the Solow-Swan equation.