Analysis of Solow-Swan model with nonlocal fractional derivative operator
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| Format: | Preprint |
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2025
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| _version_ | 1866916890072317952 |
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| author | Aibinu, MO Duffy, KJ Moyo, S |
| author_facet | Aibinu, MO Duffy, KJ Moyo, S |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_06883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of Solow-Swan model with nonlocal fractional derivative operator Aibinu, MO Duffy, KJ Moyo, S Functional Analysis Analysis of PDEs 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. |
| title | Analysis of Solow-Swan model with nonlocal fractional derivative operator |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2508.06883 |