Approximate analytical solution for seepage flow with fractional derivatives in porous media.

*(English)*Zbl 0942.76077Summary: We propose an exact model for seepage flow in porous media with fractional derivatives, which modifies the well-known Darcy law and overcomes the continuity assumption of seepage flow. A variational iteration method is described and used to give approximate solutions of the problem. The results show that the proposed iteration method, requiring no linearization or small perturbation, is effective.

##### MSC:

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

76M30 | Variational methods applied to problems in fluid mechanics |

##### Keywords:

seepage flow; porous media; fractional derivatives; Darcy law; variational iteration method; approximate solutions
PDF
BibTeX
XML
Cite

\textit{J. He}, Comput. Methods Appl. Mech. Eng. 167, No. 1--2, 57--68 (1998; Zbl 0942.76077)

Full Text:
DOI

##### References:

[1] | He, J.H., A new approach to nonlinear partial differential equations, Comm. nonlinear sci. numer. simul., 2, 4, 230-235, (1997), IP address in Internet: |

[2] | He, J.H., Variational iteration method for delay differential equations, Comm. nonlinear sci. numer. simul., 2, 4, 235-236, (1997) |

[3] | He, J.H., A variational iteration method for nonlinearity and its applications, Mech. practice, 20, 1, 30-32, (1998), (in Chinese) |

[4] | He, J.H., Variational iteration approach to 2-spring system, Mech. sci. technol., 17, 2, 221-223, (1998) |

[5] | Delbosco, D., Existence and uniqueness for a nonlinear fractional differential equation, J. math. anal. appl., 204, 2, 609-612, (1996) · Zbl 0881.34005 |

[6] | Huang, A.X., A new decomposition for solving percolation equations in porous media, (), 417-420 |

[7] | Inokuti, M., General use of the Lagrange multiplier in nonlinear mathematical physics, (), 156-162 |

[8] | Finlayson, B.A., The method of weighted residuals and variational principles, (1972), Academic Press · Zbl 0319.49020 |

[9] | Adomian, G., A review of the decomposition method in applied mathematics, J. math. anal. applic., 135, 510-513, (1988) · Zbl 0671.34053 |

[10] | Campos, L.M.B.C., On the solution of some simple fractional differential equations, Int. J. math. math. sci., 13, 3, 481-496, (1990) · Zbl 0711.34019 |

[11] | Duarte, R.T., A new technique for the analysis of strong ground vibrations and the quantification of earthquake actions, () |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.