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Numerical Solutions of a Variable-Order Fractional Financial System

Author

Listed:
  • Shichang Ma
  • Yufeng Xu
  • Wei Yue

Abstract

The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. Moreover, the stable equilibrium point, quasiperiodic trajectory, and chaotic attractor are found in the variable-order fractional financial system with proper order functions.

Suggested Citation

  • Shichang Ma & Yufeng Xu & Wei Yue, 2012. "Numerical Solutions of a Variable-Order Fractional Financial System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, September.
    • Handle: RePEc:hin:jnljam:417942
    DOI: 10.1155/2012/417942
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    Cited by:

    1. Souad Bensid Ahmed & Adel Ouannas & Mohammed Al Horani & Giuseppe Grassi, 2022. "The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    2. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    3. Giresse, Tene Alain & Crepin, Kofane Timoleon & Martin, Tchoffo, 2019. "Generalized synchronization of the extended Hindmarsh–Rose neuronal model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 311-319.
    4. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.

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