Dynamical behaviour of fractional-order finance system

Abstract

In this paper, we developed the fractional-order finance system transmission model. The main objective of this paper is to construct and evaluate a fractional derivative to track the shape of the dynamic chaotic financial system of fractional order. The numerical solution for fractional-order financial system is determined using the Atangana–Baleanu–Caputo (ABC) and Caputo derivatives. Picard–Lindelof’s method shows the existence and uniqueness of the solution. Numerical techniques show that ABC derivative strategy can be used effectively to overcome the risk of investment. An active control strategy for controlling chaos is used in this system. The stabilisation of equilibrium is obtained by both theoretical analysis and simulation results.

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Correspondence to Ali Akgül.

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Farman, M., Akgül, A., Saleem, M.U. et al. Dynamical behaviour of fractional-order finance system. Pramana - J Phys 94, 164 (2020). https://doi.org/10.1007/s12043-020-02030-8

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Keywords

  • Finance system
  • fractional derivative
  • Picard–Lindelof
  • stability analysis
  • price index

PACS nos

  • 02.30.Hq
  • 02.60.Cb
  • 02.30.Gp