Analysis of Solow-Swan model with nonlocal fractional derivative operator

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.