MODELING OF TELECOMMUNICATION REVENUE AS A PERCENTAGE OF GROSS DOMESTIC PRODUCT’S FOR COUNTRIES WITH FRACTIONAL CALCULUS

Year 2021, Volume: 6 Issue: 1, 28 - 34, 29.06.2021

Nisa Özge Önal Tuğrul Esra Ergün Deniz Can Köseoğlu Kamil Karacuha Kevser Şimşek Ertugrul Karacuha

https://doi.org/10.52876/jcs.911144

Cited By: 1

Abstract

This study explores the modeling of the share of telecommunication revenues in gross domestic product from the year 2000 to 2018 for 5 countries including France, Germany, Italy, Turkey, the UK, and the OECD average. First, a new mathematical model based on Fractional Calculus and Least Square Method is proposed. Later, the telecommunication revenues in GDP dataset is modeled. Further, we compare the new Fractional approach to the classical Polynomial approach in three different settings. The results show that employing Fractional Calculus yields better modeling performance when compared to the classical Polynomial Approach in terms of Mean Absolute Percentage Error (MAPE). The Fractional approach outperforms the Polynomial approach by 0.1329 % MAPE on average. The largest MAPE is found for Turkey while the smallest MAPE is obtained for Italy in all settings.

Keywords

Fractional Calculus, GDP, MAPE, Modelling, Telecommunication Revenue

Supporting Institution

İTÜ VODAFONE FUTURE LAB

Project Number

ITUVF20180901P11

Thanks

This work is supported in part by Istanbul Technical University (ITU) Vodafone Future Lab under Project No. ITUVF20180901P11.

References

• [1] Regulations, R. International Telecommunication Union Std., November 2012. Online Available: http://www. itu. int/pub. RREG-RR/en. (accessed 7 June 2020).
• [2] ITU. Constitution and Convention of the International Telecommunication Union. Online Available: http://handle.itu.int/11.1004/020.2000/s.020, (accessed 9 June 2020).
• [3] Tarasov, V. E. On history of mathematical economics: Application of fractional calculus. Mathematics, 2019, 7(6), 509.
• [4] Schumpeter, J. A., & Joseph, A. The Nature and Essence of Theoretical Economics. Dunker & Humblot. 1908. [5] Hayes, M. The Economics of Keynes: A new guide to the General Theory. Edward Elgar Publishing. 2008, 2–17.
• [6] Samko, S.G.; Kilbas, A.A.; Marichev, O.I. Fractional Integrals and Derivatives Theory and Applications; Gordon and Breach: New York, NY, USA, 1993; 1006p.
• [7] Kiryakova, V. Generalized Fractional Calculus and Applications; Longman and John Wiley: New York, NY, USA, 1994; 360p.
• [8] Podlubny, I. Fractional Differential Equations; Academic Press: San Diego, CA, USA, 1998; 340p.
• [9] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J. Theory and Applications of Fractional Differential Equations; Elsevier: Amsterdam, The Netherlands, 2006; 540p.
• [10] Diethelm, K. The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type; Springer: Berlin, Germany, 2010; 247p.
• [11] Letnikov, A.V. On the historical development of the theory of differentiation with arbitrary index. Math. Collect. 1868, 3, 85–112. (In Russian).
• [12] Ross, B. ‘A brief history and exposition of the fundamental theory of fractional calculus. In Fractional Calculus and Its Applications’ Proceedings of the International Conference Held at the University of New Haven, June 1974; Series: Lecture Notes in Mathematics; Springer: Berlin/Heidelberg, Germany, 1975; Volume 457, pp. 1–36.
• [13] Ross, B. The development of fractional calculus 1695–1900. Hist. Math. 1977, 4, 75–89.
• [14] Ross, B. Fractional Calculus. Math. Mag. 1977, 50, 115–122.
• [15] Kiryakova, V. A brief story about the operators of the generalized fractional calculus. Fract. Calc. Appl. Anal. 2008, 11, 203–220.
• [16] Tenreiro Machado, J.; Kiryakova, V.; Mainardi, F. Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 2011, 16, 1140–1153.
• [17] Tenreiro Machado, J.A.; Galhano, A.M.; Trujillo, J.J. Science metrics on fractional calculus development since 1966. Fract. Calc. Appl. Anal. 2013, 16, 479–500.
• [18] Önal, N. Ö., Karaçuha, K., Erdinç, G. H., Karaçuha, B. B., & Karaçuha, E. A mathematical approach with fractional calculus for the modeling of children’s physical development. Computational and mathematical methods in medicine, 2019.
• [19] Karaçuha, E., Önal, N. Ö., Ergün, E., Tabatadze, V., Alkaş, H., Karaçuha, K., Tontus, Ö. & Nu, N. V. N. Modeling and Prediction of the Covid-19 Cases With Deep Assessment Methodology and Fractional Calculus. IEEE Access, 2020, 8, 164012-164034.
• [20] Karaçuha, E., Tabatadze, V., Karacuha, K., Önal, N. Ö., & Ergün, E. Dee p Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries. Mathematics, 2020, 8(4), 633. [21] Herrmann, R. Fractional calculus: an introduction for physicists; New Jersey: World Scientific, 2014.
• [22] OECD Key ICT Indicators. Telecommunication Revenue, Online Available: oecd.org/internet/broadband/oecdkeyictindicators.htm (accessed 25 Feb 2020).
• [23] Worldbank World Development Indicators. GDP (current US$). Online Available: https://databank.worldbank.org/source/world-development-indicators (accessed 25 Feb 2020).
• [24] De Myttenaere, A., Golden, B., Le Grand, B., & Rossi, F. Mean absolute percentage error for regression models. Neurocomputing, 2016, 192, 38-48.