Applying Fractional Calculus to Analyze Economic Growth Modelling

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In this work, we apply fractional calculus to analyze a class of economic growth modelling (EGM) of the Spanish economy. More precisely, the Grünwald-Letnnikov and Caputo derivatives are used to simulate GDP by replacing the previous integer order derivatives with the help of Matlab, SPSS and R software. As a result, we find that the data raised from the Caputo derivative are better than the data raised from the Grünwald-Letnnikov derivative. We improve the previous result in [12].

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  • [1] K. Diethelm The Analysis of Fractional Differential Equations Lecture Notes in Mathematics Springer New York 2010.

  • [2] Y. Zhou J. Wang L. Zhang Basic Theory of Fractional Differential Equations 2nd Edn World Scientifc Singapore 2016.

  • [3] Y. Zhou Fractional Evolution Equations and Inclusions: Analysis and control Academic Press 2016.

  • [4] R. P. Agarwal S. Hristova D. O’Regan A survey of Lyapunov functions stability and impulsive Caputo fractional differential equations Fract. Calc. Appl. Anal. 19(2016) 290-318.

  • [5] J. Wang M. Fečkan Y. Zhou A survey on impulsive fractional differential equations Fract. Calc. Appl. Anal. 19(2016) 806-831.

  • [6] J. Wang X. Li Ulam-Hyers stability of fractional Langevin equations Appl. Math. Comput. 258(2015) 72-83.

  • [7] J. Wang X. Li A uniformed method to Ulam-Hyers stability for some linear fractional equations Mediterr. J. Math. 13(2016) 625-635.

  • [8] M. Li J. Wang Finite time stability of fractional delay differential equations Appl. Math. Lett. 64(2017) 170-176.

  • [9] J. Wang M. Fečkan Y. Zhou Center stable manifold for planar fractional damped equations Appl. Math. Comput. 296(2017) 257-269.

  • [10] A. A. Kilbas H. M. Srivastava J. J. Trujillo Theory and Applications of Fractional Differential Equations Elsevier Amsterdam 2006.

  • [11] R. Hilfer Applications of Fractional Calculus in Physics World Scientific Singapore 1999.

  • [12] I. Tejado D. Valério E. Pérez N. Valério Fractional calculus in economic growth modelling: the Spanish and Portuguese cases Int. J. Dyn. Control 5(2017) 208-222.

  • [13] J. A. T. Machado M. E. Mata A fractional perspective to the bond graph modelling of world economies Nonlinear Dyn. 80(2015) 1839-1852.

  • [14] J. A. T. Machado M. E. Mata A. M. Lopes Fractional state space analysis of economic systems Entropy 17(2015) 5402-5421.

  • [15] J. A. T. Machado M. E. Mata Pseudo phase plane and fractional calculus modeling of western global economic downturn Commun. Nonlinear Sci. Numer. Simulat. 22(2015) 396-406.

  • [16] V. V. Tarasova V. E. Tarasov Elasticity for economic processes with memory: Fractional differential calculus approach Fract. Diff. Calc. 6(2016) 219-232.

  • [17] S. A. David J. A. T. Machado D. D. Quintino J. M. Balthazar Partial chaos suppression in a fractional order macroeconomic model Math. Comput. Simul. 122(2016) 55-68.

  • [18] T. Škovránek I. Podlubny I. Petráš Modeling of the national economies in state-space: A fractional calculus approach Economic Modelling 29(2012) 1322-1327.

  • [19] I. Petras I. Podlubny State space description of national economies: The V4 countries Computational Statistics & Data Analysis 52(2007) 1223-1233.

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