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Tytuł artykułu

Economic growth in the European Union modelled with fractional derivatives: first results

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents models of economic growth for all states of the European Union (EU), since either 1970 or the year of accession to the EU. Both integer and fractional order models are obtained, where the gross domestic product (GDP) is a function of the country’s land area, gross capital formation (GCF), exports of goods and services, and average years of school attendance.
Rocznik
Strony
455--465
Opis fizyczny
Bibliogr. 34 poz., wykr., tab.
Twórcy
autor
  • Industrial Engineering School, University of Extremadura, Avda. de Elvas, s/n, 06006 Badajoz, Spain
autor
  • Industrial Engineering School, University of Extremadura, Avda. de Elvas, s/n, 06006 Badajoz, Spain
autor
  • IDMEC, Instituto Superior T´ecnico, Universidade de Lisboa, Lisboa, Portugal, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
Bibliografia
  • [1] Y. Hu and B. Oksendal, “Fractional white noise calculus and applications to finance”, Infinite Dimensional Analysis, Quantum Probability and Related Topics 6(1), 2003.
  • [2] I. Petr´as and I. Podlubny, “State space description of national economies: The V4 countries”, Computational Statistics & Data Analysis 52(2), 1223–1233 (2007).
  • [3] T. Skovranek, I. Podlubny, and I. Petr´as, “Modeling of the national economies in state-space: A fractional calculus approach”, Economic Modelling 29(4), 1322–1327 (2012).
  • [4] Y. Xu and Z. He, “Synchronization of variable-order fractional financial system via active control method”, Central European Journal of Physics 11(6), 824–835 (2013).
  • [5] Y. Yue, L. He, and G. Liu, “Modeling and application of a new nonlinear fractional financial model”, Journal of Applied Mathematics 2013, 1–9 (2013).
  • [6] D.E. Bloom, D. Canning, and J. Sevilla, Technological diffusion, conditional convergence, and economic growth, 2002.
  • [7] S. Sassia and M. Goaied, “Financial development, ICT diffusion and economic growth: Lessons from MENA region”, Telecommunications Policy 37(4–5), 252–261 (2013).
  • [8] A. Seck, “International technology diffusion and economic growth: Explaining the spillover benefits to developing countries”, Structural Change and Economic Dynamics 23(4), 437–451 (2012).
  • [9] R.L. Magin, Fractional Calculus in Bioengineering, Begell House, 2004.
  • [10] B. Baeumer and M.M. Meerschaert, “Fractional diffusion with two time scales”, Physica A: Statistical Mechanics and its Applications 373, 237–251 (2007).
  • [11] J. Blackledge, “Application of the fractal market hypothesis for modelling macroeconomic time series”, ISAST Transactions on Electronics and Signal Processing 2(1), 89–110 (2008).
  • [12] J. Blackledge, “Application of the fractional diffusion equation for predicting market behaviour”, International Journal of Applied Mathematics 40(3), 130–158 (2010).
  • [13] M. Boleantu, “Fractional dynamical systems and applications in economy”, Differential Geometry – Dynamical Systems 10, 62–70 (2008).
  • [14] ´A. Cartea and D. del Castillo-Negrete, “Fractional diffusion models of option prices in markets with jumps”, Physica A: Statistical Mechanics and its Applications 374(2), 749–763 (2007).
  • [15] S.A. David, J.A.T. Machado, D.D. Quintino, and J.M. Balthazar, “Partial chaos suppression in a fractional order macroeconomic model”, Mathematics and Computers in Simulation 122, 55–68 (2016).
  • [16] R. Gorenflo, F. Mainardi, E. Scalas, and M. Raberto, Mathematical Finance Trends in Mathematics, chapter Fractional Calculus and Continuous-Time Finance III: the Diffusion Limit, pages 171–180, Birkh¨auser Basel, 2001.
  • [17] N. Laskin, “Fractional market dynamics”, Physica A: Statistical Mechanics and its Applications 287, 482–492 (2000).
  • [18] F.Mainardi, M. Raberto, R. Gorenflo, and E. Scalas, “Fractional calculus and continuous-time finance II: The waiting-time distribution”, Physica A: Statistical Mechanics and its Applications 287, 468–481 (2000).
  • [19] O. Marom and E. Momoniat, “A comparison of numerical solutions of fractional diffusion models in finance”, Nonlinear Analysis: Real World Application 10, 3435–3442 (2009).
  • [20] M.M. Meerschaert and E. Scalas, “Coupled continuous time random walks in finance”, Physica A: Statistical Mechanics and its Applications 370, 114–118 (2006).
  • [21] M.M. Meerschaert and A. Sikorski, Stochastic Models for Fractional Calculus, volume 43 of Studies in Mathematics, Walter de Gruyter & Co, 2012.
  • [22] E. Scalas, “The application of continuous-time random walks in finance and economics”, Physica A: Statistical Mechanics and its Applications 362, 225–239 (2006).
  • [23] E. Scalas, R. Gorenflo, and F. Mainardi, “Fractional calculus and continuous-time finance”, Physica A: Statistical Mechanics and its Applications 284(1–4), 376–384 (2000).
  • [24] V.V. Tarasova and V.E. Tarasov, “Economic interpretation of fractional derivatives”, Progress in Fractional Differentiation and Applications 1, 1–6 (2017).
  • [25] V.E. Tarasov, “Long and short memory in economics: Fractional-order difference and differentiation”, IRA – International Journal of Management and Social Sciences 5(2), 327–334 (2016).
  • [26] J.A.T. Machado and M.E. Mata, “Pseudo phase plane and fractional calculus modeling of western global economic downturn”, Communications in Nonlinear Science and Numerical Simulation 22(1–3), 396–406 (2015).
  • [27] J.A. Tenreiro Machado, M.E. Mata, and A.M. Lopes, “Fractional state space analysis of economic systems”, Entropy 17, 5402–5421 (2015).
  • [28] I. Tejado, D. Val´erio, E. P´erez, and N. Val´erio, “Fractional calculus in economic growth modelling: The economies of France and Italy”, in International Conference on Fractional Differentiation and its Applications, 2016.
  • [29] I. Tejado, D. Val´erio, E. P´erez, and N. Val´erio, “Fractional calculus in economic growth modelling. The Spanish and Portuguese cases”, International Journal of Dynamics and Control 5(1), 208–222 (2017).
  • [30] D. Val´erio and J. S´a da Costa, An Introduction to Fractional Control, IET, Stevenage, 2013, ISBN 978-1-84919-545-4.
  • [31] World Bank, World development indicators, 2017, Last Updated: 07/20/2017. Access Date: 07/25/2017.
  • [32] J.-W. Lee and H. Lee, “Lee and Lee long-run education dataset”, 2016, Last Updated: 01/01/2016. Access Date: 06/26/2017.
  • [33] World Bank, Education statistics – All indicators, 2017, Last Updated: 05/25/2017. Access date: 06/29/2017.
  • [34] Wittgenstein Centre for Demography and Global Human Capital, Wittgenstein centre data explorer version 1.2, 2015, Access Date: 07/05/2017.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cf1c06ed-d4d1-4cd3-b18b-d20173111574
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