Approximate solutions of fractional nonlinear equations using homotopy perturbation transformation method.

*(English)*Zbl 1242.65136Summary: A homotopy perturbation transformation method which is based on homotopy perturbation method and Laplace transform is first applied to solve the approximate solution of fractional nonlinear equations. The nonlinear terms can be easily handled by the use of He’s polynomials. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

##### MSC:

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

65L99 | Numerical methods for ordinary differential equations |

34A08 | Fractional ordinary differential equations |

44A10 | Laplace transform |

34A34 | Nonlinear ordinary differential equations and systems |

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

##### Keywords:

numerical examples; homotopy perturbation transformation method; Laplace transform; fractional nonlinear equation; convergence
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\textit{Y. Liu}, Abstr. Appl. Anal. 2012, Article ID 752869, 14 p. (2012; Zbl 1242.65136)

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