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A fractional model for the dynamics of competition between commercial and rural banks in Indonesia

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  • Fatmawati,
  • Khan, Muhammad Altaf
  • Azizah, Muftiyatul
  • Windarto,
  • Ullah, Saif

Abstract

In the present paper, we propose a mathematical model that describes the dynamics of competition between commercial and rural banks in Indonesia through two different fractional operators Atangana-Baleanu and Caputo. We present a parameter estimation of the Lotka–Volterra competition model by using the genetic algorithm method. Parameter estimation is done based on annual profit data of commercial and rural banks in Indonesia. The estimation results capable to predict the profit of commercial and rural banks every year which is not much different from the real data. Next, the competition model between commercial and rural banks in Indonesia is explored in the fractional sense of Atangana–Baleanu and Caputo derivative. The fractional model is examined through the Atangana–Baleanu and Caputo fractional derivative and present the results. A recent numerical procedure is used to obtain the graphical results using various values of the fractional order parameter for the dynamics of the model. A comparison of both the operators for various values of the fractional order parameters are given. We discussed briefly the results and then summarized briefly in section conclusion.

Suggested Citation

  • Fatmawati, & Khan, Muhammad Altaf & Azizah, Muftiyatul & Windarto, & Ullah, Saif, 2019. "A fractional model for the dynamics of competition between commercial and rural banks in Indonesia," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 32-46.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:32-46
    DOI: 10.1016/j.chaos.2019.02.009
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    References listed on IDEAS

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    Cited by:

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    3. Boudaoui, Ahmed & El hadj Moussa, Yacine & Hammouch, Zakia & Ullah, Saif, 2021. "A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Wang, Wanting & Khan, Muhammad Altaf & Fatmawati, & Kumam, P. & Thounthong, P., 2019. "A comparison study of bank data in fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 369-384.
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    7. Yin, Wei & Hua, Qiulan & Kirkulak-Uludag, Berna, 2025. "To compete or cooperate: The application of system dynamics simulation on the choice of Chinese banks," Journal of Behavioral and Experimental Finance, Elsevier, vol. 45(C).
    8. Vázquez-Guerrero, P. & Gómez-Aguilar, J.F. & Santamaria, F. & Escobar-Jiménez, R.F., 2019. "Synchronization patterns with strong memory adaptive control in networks of coupled neurons with chimera states dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 167-175.
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    10. Li, Zhongfei & Liu, Zhuang & Khan, Muhammad Altaf, 2020. "Fractional investigation of bank data with fractal-fractional Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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