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**Numerical solutions of a variable-order fractional financial system.**
*(English)*
Zbl 1251.91070

Summary: 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.

### MSC:

91G60 | Numerical methods (including Monte Carlo methods) |

35R11 | Fractional partial differential equations |

35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

### Keywords:

numerical solution; variable-order fractional financial system; Adams-Bashforth-Moulton method
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\textit{S. Ma} et al., J. Appl. Math. 2012, Article ID 417942, 14 p. (2012; Zbl 1251.91070)

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