Paper: arXiv 2508.20100

Authors: M. O. Aibinu, K. J. Duffy, S. Moyo

Abstract

The Solow-Swan equation is a cornerstone in the development of modern economic growth theory and continues to attract significant scholarly attention. This study incorporates memory effects into the classical Solow-Swan model by introducing a formulation based on the Caputo fractional derivative. A comparative analysis is conducted between the integer-order and fractional-order versions of the model to examine the influence of fractional dynamics on capital accumulation. The findings reveal that the inclusion of a fractional-order derivative significantly affects the trajectory and long-term stability of capital, offering a more flexible and comprehensive framework for modeling economic growth processes.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper applies non-integer order calculus (Caputo fractional derivatives, Sumudu transforms, Adomian decomposition) to the classical Solow-Swan economic growth model to model memory effects. However, it lacks empirical rigor, relying solely on theoretical MATLAB simulations with arbitrary calibration parameters rather than real-world data estimation or backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Incorporate Memory Effects into Solow-Swan Growth Model] --> B[Model Formulation: Classical Solow-Swan + Caputo Fractional Derivative]
    B --> C[Inputs: Production Functions, Savings Rate, Depreciation, Fractional Order α]
    C --> D[Comparative Analysis: Integer-Order vs. Fractional-Order Dynamics]
    D --> E[Simulations: Trajectory & Stability Analysis of Capital Accumulation]
    E --> F[Key Outcome: Fractional Derivative Alters Capital Trajectory & Long-Term Stability]

Cited References (32)

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  4. Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method (2022) — link
  5. Parameter estimation of the Solow–Swan fundamental differential equation (2022) — link
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  7. Mathematical Economics: Application of Fractional Calculus (2020) — link
  8. Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction (2020) — link
and 24 more
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  2. A New Iterational Method for Ordinary Equations Using Sumudu Transform (2016) — link
  3. The role of education in economic growth: theory, history and current returns (2013) — link
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  23. Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, SK, Canada
  24. The asymmetric effect of natural disasters on economic growth in Iran: the NARDL approach within the framework of the Solow-Swan Theory

0 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.