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Conformable Derivative Approach to Gross Domestic Product Model with Real Data of World Bank

Year 2020, Volume: 7 Issue: 1, 1 - 9, 28.06.2020
https://doi.org/10.35193/bseufbd.640361

Abstract

In this study, we consider gross domestic product (GDP) model within conformable derivative. In view of real data from the Republic of Korea, the European Union and the United States of America taken from World Bank [20] between 1960-2018 by simulations and error analysis, we obtain an analytical solution of the conformable GDP model and compare the findings with the integer order GDP model.

References

  • Khalil, R., Horani, M.A., Yousef, A., Sababheh, M., A new definition of fractional derivative, J. Comput. App. Math., 264, 65-70, 2014.
  • Abdeljawad, T. On conformable fractional calculus, Journal of Computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.
  • Atangana, A., Baleanu, D., & Alsaedi, A. (2015). New properties of conformable derivative. Open Mathematics, 13(1).
  • Katugampola, U.N., A New Fractional Derivative with Classical Properties, arXiv:1410.6535v2., 2014.
  • Anderson, D. R., Ulness, D. J. (2015). Newly defined conformable derivatives. Adv. Dyn. Syst. Appl, 10(2), 109-137.
  • World Bank: World Development Indicators. https://databank.worldbank.orgreports.aspx?source=2&country=&series=NY.GDP.PCAP.CD&period=#. Accessed 14 October 2019.
  • Bas, E., Acay, B., Ozarslan, R. (2019). The price adjustment equation with different types of conformable derivatives in market equilibrium. AIMS Mathematics, 4(3), 805.
  • Yusuf, A., Aliyu, A. I., & Baleanu, D. (2018). Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics. Optical and Quantum Electronics, 50(4), 190.
  • Ortega, A., Rosales, J. J. (2018). Newton’s law of cooling with fractional conformable derivative. Revista mexicana de física, 64(2), 172-175.
  • Yavuz, M., Yaşkıran, B. (2018). Homotopy methods for fractional linear/nonlinear differential equations with a local derivative operator. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(3), 75-89.
  • Atangana, A., and Baleanu, D., 2016. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Thermal Science, 20, 757-763.
  • Caputo, M., Fabrizio, M., 2015. A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1, 1-13.
  • Qureshi, S., Yusuf, A. (2019). Fractional derivatives applied to MSEIR problems: Comparative study with real world data. The European Physical Journal Plus, 134(4), 171.
  • Qureshi, S., Yusuf, A. (2019). Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu. Chaos, Solitons & Fractals, 122, 111-118.
  • Ozarslan, R., Ercan, A., Bas, E. (2019). Novel Fractional Models Compatible with Real World Problems. Fractal and Fractional, 3(2), 15.
  • Bas, E., Ozarslan, R. (2018). Real world applications of fractional models by Atangana-Baleanu fractional derivative. Chaos, Solitons and Fractals, 116, 121-125.
  • Bas, E., Metin, F. (2013). Fractional singular Sturm-Liouville operator for Coulomb potential. Advances in Difference Equations, 2013(1), 300.
  • Bas, E., Metin, F. (2015). Spectral analysis for fractional hydrogen atom equation. Advances in Pure Mathematics, 5(13), 767.
  • Almeida, R. (2017). What is the best fractional derivative to fit data?. Applicable Analysis and Discrete Mathematics, 11(2), 358-368.
  • Yokuş, A. (2018). Comparison of Caputo and conformable derivatives for time-fractional Korteweg–de Vries equation via the finite difference method. International Journal of Modern Physics B, 32(29), 1850365.
  • Bulut, H., Sulaiman, T. A., & Baskonus, H. M. (2018). Dark, bright optical and other solitons with conformable space-time fractional second-order spatiotemporal dispersion. Optik, 163, 1-7.

Dünya Bankası Reel Verileri İle Gayri Safi Yurtiçi Hasıla Modeline Conformable Türev Yaklaşımı

Year 2020, Volume: 7 Issue: 1, 1 - 9, 28.06.2020
https://doi.org/10.35193/bseufbd.640361

Abstract

Bu çalışmada, conformable
türev yardımıyla gayri safi yurtiçi hasıla (GSYİH) modelini ele alıyoruz.
Conformable GSYİH modelinin analitik çözümünü elde ediyor ve sonuçları, 1960-2018
yılları arasında Dünya Bankası'ndan [20] alınan Kore Cumhuriyeti, Avrupa Birliği
ve Amerika Birleşik Devletleri’nin reel verilerini göz önüne alarak tam
mertebeden GSYİH modeliyle, simülasyonlar ve hata analizleri yardımıyla karşılaştırıyoruz

References

  • Khalil, R., Horani, M.A., Yousef, A., Sababheh, M., A new definition of fractional derivative, J. Comput. App. Math., 264, 65-70, 2014.
  • Abdeljawad, T. On conformable fractional calculus, Journal of Computational and Applied Mathematics, vol. 279, pp. 57-66, 2015.
  • Atangana, A., Baleanu, D., & Alsaedi, A. (2015). New properties of conformable derivative. Open Mathematics, 13(1).
  • Katugampola, U.N., A New Fractional Derivative with Classical Properties, arXiv:1410.6535v2., 2014.
  • Anderson, D. R., Ulness, D. J. (2015). Newly defined conformable derivatives. Adv. Dyn. Syst. Appl, 10(2), 109-137.
  • World Bank: World Development Indicators. https://databank.worldbank.orgreports.aspx?source=2&country=&series=NY.GDP.PCAP.CD&period=#. Accessed 14 October 2019.
  • Bas, E., Acay, B., Ozarslan, R. (2019). The price adjustment equation with different types of conformable derivatives in market equilibrium. AIMS Mathematics, 4(3), 805.
  • Yusuf, A., Aliyu, A. I., & Baleanu, D. (2018). Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics. Optical and Quantum Electronics, 50(4), 190.
  • Ortega, A., Rosales, J. J. (2018). Newton’s law of cooling with fractional conformable derivative. Revista mexicana de física, 64(2), 172-175.
  • Yavuz, M., Yaşkıran, B. (2018). Homotopy methods for fractional linear/nonlinear differential equations with a local derivative operator. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(3), 75-89.
  • Atangana, A., and Baleanu, D., 2016. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, Thermal Science, 20, 757-763.
  • Caputo, M., Fabrizio, M., 2015. A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl, 1, 1-13.
  • Qureshi, S., Yusuf, A. (2019). Fractional derivatives applied to MSEIR problems: Comparative study with real world data. The European Physical Journal Plus, 134(4), 171.
  • Qureshi, S., Yusuf, A. (2019). Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu. Chaos, Solitons & Fractals, 122, 111-118.
  • Ozarslan, R., Ercan, A., Bas, E. (2019). Novel Fractional Models Compatible with Real World Problems. Fractal and Fractional, 3(2), 15.
  • Bas, E., Ozarslan, R. (2018). Real world applications of fractional models by Atangana-Baleanu fractional derivative. Chaos, Solitons and Fractals, 116, 121-125.
  • Bas, E., Metin, F. (2013). Fractional singular Sturm-Liouville operator for Coulomb potential. Advances in Difference Equations, 2013(1), 300.
  • Bas, E., Metin, F. (2015). Spectral analysis for fractional hydrogen atom equation. Advances in Pure Mathematics, 5(13), 767.
  • Almeida, R. (2017). What is the best fractional derivative to fit data?. Applicable Analysis and Discrete Mathematics, 11(2), 358-368.
  • Yokuş, A. (2018). Comparison of Caputo and conformable derivatives for time-fractional Korteweg–de Vries equation via the finite difference method. International Journal of Modern Physics B, 32(29), 1850365.
  • Bulut, H., Sulaiman, T. A., & Baskonus, H. M. (2018). Dark, bright optical and other solitons with conformable space-time fractional second-order spatiotemporal dispersion. Optik, 163, 1-7.
There are 21 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ramazan Ozarslan 0000-0002-7285-7308

Publication Date June 28, 2020
Submission Date October 31, 2019
Acceptance Date April 13, 2020
Published in Issue Year 2020 Volume: 7 Issue: 1

Cite

APA Ozarslan, R. (2020). Conformable Derivative Approach to Gross Domestic Product Model with Real Data of World Bank. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 7(1), 1-9. https://doi.org/10.35193/bseufbd.640361