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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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    4. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
    5. Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
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    Cited by:

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    3. 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. Ishtiaq Ali & Sami Ullah Khan, 2023. "A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
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    9. Al-khedhairi, A. & Elsadany, A.A. & Elsonbaty, A., 2019. "Modelling immune systems based on Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 25-39.

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