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Macroeconomic models with long dynamic memory: Fractional calculus approach

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  • Tarasov, Vasily E.
  • Tarasova, Valentina V.

Abstract

This article discusses macroeconomic models, which take into account effects of power-law fading memory. The power-law long memory is described by using the mathematical tool of fractional calculus that includes the fractional derivatives and integrals of non-integer orders. We obtain solutions of the fractional differential equations of these macroeconomic models. Examples of dependence of macroeconomic dynamics on the memory effects are suggested. Asymptotic behaviors of the solutions, which characterize the rate of technological growth with memory, are described. We formulate principles of economic dynamics with one-parametric and multi-parametric memory. It has been shown that the effects of fading long memory can change the economic growth rate and change dominant parameters, which determine growth rates.

Suggested Citation

  • Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:466-486
    DOI: 10.1016/j.amc.2018.06.018
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    Cited by:

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    2. Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
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    4. José A. Tenreiro Machado & Maria Eugénia Mata & António M. Lopes, 2020. "Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes," Mathematics, MDPI, vol. 8(1), pages 1-17, January.
    5. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    6. Vasily E. Tarasov, 2020. "Non-Linear Macroeconomic Models of Growth with Memory," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    7. Chu, Yu-Ming & Bekiros, Stelios & Zambrano-Serrano, Ernesto & Orozco-López, Onofre & Lahmiri, Salim & Jahanshahi, Hadi & Aly, Ayman A., 2021. "Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. Vasily E. Tarasov & Valentina V. Tarasova, 2019. "Dynamic Keynesian Model of Economic Growth with Memory and Lag," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    9. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    10. Xiang, Guangjian & Yin, Deshun & Cao, Chenxi & Gao, Yunfei, 2021. "Creep modelling of soft soil based on the fractional flow rule: Simulation and parameter study," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    11. Ertuğrul Karaçuha & Vasil Tabatadze & Kamil Karaçuha & Nisa Özge Önal & Esra Ergün, 2020. "Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    12. Xu Wang & JinRong Wang & Michal Fečkan, 2020. "BP Neural Network Calculus in Economic Growth Modelling of the Group of Seven," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    13. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    14. Mohamed I. Abbas & Snezhana Hristova, 2021. "On the Initial Value Problems for Caputo-Type Generalized Proportional Vector-Order Fractional Differential Equations," Mathematics, MDPI, vol. 9(21), pages 1-10, October.
    15. Tarasov, Vasily E., 2020. "Fractional econophysics: Market price dynamics with memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
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    17. Tomas Skovranek, 2019. "The Mittag-Leffler Fitting of the Phillips Curve," Mathematics, MDPI, vol. 7(7), pages 1-11, July.

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