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**Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations.**
*(English)*
Zbl 1219.65081

Summary: Linear and nonlinear boundary value problems for fourth-order fractional integro-differential equations are solved by variational iteration method and homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The solutions of both problems are derived by infinite convergent series which are easily computable and then graphical representation shows that both methods are most effective and convenient one to solve linear and nonlinear boundary value problems for fourth-order fractional integro-differential equations.

### MSC:

65L99 | Numerical methods for ordinary differential equations |

34A08 | Fractional ordinary differential equations |

34K25 | Asymptotic theory of functional-differential equations |

34K37 | Functional-differential equations with fractional derivatives |

45J05 | Integro-ordinary differential equations |

### Keywords:

variational iteration method; homotopy perturbation method; boundary value problems; integro-differential equations; Caputo fractional derivative
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\textit{Y. Nawaz}, Comput. Math. Appl. 61, No. 8, 2330--2341 (2011; Zbl 1219.65081)

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### References:

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