A novel solution for fractional chaotic Chen system. (English) Zbl 1326.65101

Alomari, A. K.

J. Nonlinear Sci. Appl. 8, No. 5, 478-488 (2015).

Summary: A novel solution to the fraction chaotic Chen system is presented in this paper by using the step homotopy analysis method. This method yields a continuous solution in terms of a rapidly convergent infinite power series with easily computable terms. Moreover, the residual error of the SHAM solution is defined and computed for each time interval. Via the computing of the residual error we observe that the accuracy of the present method tends to \(10^{-11}\) which is very high.

MSC:

65L99	Numerical methods for ordinary differential equations
34A08	Fractional ordinary differential equations
34H10	Chaos control for problems involving ordinary differential equations

Keywords:

chaotic system; fractional Chen system; homotopy analysis method; step homotopy analysis method; residual error