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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
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