Application of multistage homotopy-perturbation method for the solutions of the chaotic fractional order systems.

*(English)*Zbl 1260.34027Summary: The multistage homotopy-perturbation method is extended to solve chaotic fractional order systems. The multistage homotopy-perturbation method is only a simple modification of the standard homotopy-perturbation method, which is applied to a sequence of intervals for finding accurate approximate analytical solutions. The fractional derivatives are described in the Caputo sense. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. Numerical results reveal that the multistage method is a promising tool for chaotic and hyperchaotic fractional order systems.

##### MSC:

34A45 | Theoretical approximation of solutions to ordinary differential equations |

34A08 | Fractional ordinary differential equations and fractional differential inclusions |

34C28 | Complex behavior and chaotic systems of ordinary differential equations |

34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |