Multivariate Padé approximation for solving nonlinear partial differential equations of fractional order.

*(English)*Zbl 1275.65088Summary: Two techniques are implemented, the Adomian decomposition method (ADM) and the multivariate Padé approximation (MPA), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation is solved and converted to a power series by the Adomian decomposition method (ADM), then the power series solution of the fractional differential equation is put into multivariate Padé series. Finally, numerical results are compared and presented in tables and figures.

##### MSC:

65N99 | Numerical methods for partial differential equations, boundary value problems |

35C10 | Series solutions to PDEs |

35R11 | Fractional partial differential equations |

41A21 | Padé approximation |

35G20 | Nonlinear higher-order PDEs |

##### Keywords:

Adomian decomposition method; multivariate Padé approximation; nonlinear partial differential equations of fractional order; power series solution; numerical results
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\textit{V. Turut} and \textit{N. Güzel}, Abstr. Appl. Anal. 2013, Article ID 746401, 12 p. (2013; Zbl 1275.65088)

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##### References:

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