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**Analytical modelling of fractional advection-dispersion equation defined in a bounded space domain.**
*(English)*
Zbl 1219.76035

Summary: The fractional advection-dispersion equation (FADE) known as its non-local dispersion, is used in groundwater hydrology and has been proven to be a reliable tool to model the transport of passive tracers carried by fluid flow in a porous media. In this paper, compact structures of FADE are investigated by means of the homotopy perturbation method with consideration of a promising scheme to calculate nonlinear terms. The problems are formulated in the Jumarie sense. Analytical and numerical results are presented.

### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

35R11 | Fractional partial differential equations |

45K05 | Integro-partial differential equations |

76S05 | Flows in porous media; filtration; seepage |

### Keywords:

fractional advection-dispersion equation; homotopy perturbation method; jumarie’s derivative### Software:

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\textit{A. Golbabai} and \textit{K. Sayevand}, Math. Comput. Modelling 53, No. 9--10, 1708--1718 (2011; Zbl 1219.76035)

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### References:

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