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Volumn 53, Issue 9-10, 2011, Pages 1708-1718

Analytical modelling of fractional advection-dispersion equation defined in a bounded space domain

Author keywords

Fractional advection dispersion equation; Homotopy perturbation method; Jumarie's derivative

Indexed keywords

ADVECTION-DISPERSION EQUATION; ANALYTICAL MODELLING; COMPACT STRUCTURES; FLUID FLOW; GROUND-WATER HYDROLOGY; HOMOTOPY PERTURBATION METHOD; JUMARIE'S DERIVATIVE; NONLINEAR TERMS; NONLOCAL; NUMERICAL RESULTS; PASSIVE TRACERS; POROUS MEDIA; SPACE DOMAIN;

EID: 79951958606     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.12.046     Document Type: Article
Times cited : (45)

References (35)
  • 4
    • 77955281742 scopus 로고    scopus 로고
    • Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients
    • Prez Guerrero J.S., Skaggs T.H. Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients. Journal of Hydrology 2010, 390:57-65.
    • (2010) Journal of Hydrology , vol.390 , pp. 57-65
    • Prez Guerrero, J.S.1    Skaggs, T.H.2
  • 5
    • 55649099424 scopus 로고    scopus 로고
    • A finite element solution for fractional advection-dispersion equation
    • Huang Q., Huang G., Zhan H. A finite element solution for fractional advection-dispersion equation. Advances in Water Resources 2008, 31:1578-1589.
    • (2008) Advances in Water Resources , vol.31 , pp. 1578-1589
    • Huang, Q.1    Huang, G.2    Zhan, H.3
  • 6
    • 76449102580 scopus 로고    scopus 로고
    • Adomian's decomposition method for solving an intermediate fractional advection-dispersion equation
    • El-Sayed A.M.A., Behiry S.H., Raslan W.E. Adomian's decomposition method for solving an intermediate fractional advection-dispersion equation. Computer and Mathematics with Applications 2010, 59:1759-1765.
    • (2010) Computer and Mathematics with Applications , vol.59 , pp. 1759-1765
    • El-Sayed, A.M.A.1    Behiry, S.H.2    Raslan, W.E.3
  • 7
    • 85112254161 scopus 로고    scopus 로고
    • Numerical solutions of the space-time fractional advection-dispersion equation
    • Momani S., Odibat Z. Numerical solutions of the space-time fractional advection-dispersion equation. Numerical Methods for Partial Differential Equations 2008, 25(5):1238-1259.
    • (2008) Numerical Methods for Partial Differential Equations , vol.25 , Issue.5 , pp. 1238-1259
    • Momani, S.1    Odibat, Z.2
  • 8
    • 71549148064 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving the space-time fractional advection-dispersion equation
    • Yildirim A., Kocak H. Homotopy perturbation method for solving the space-time fractional advection-dispersion equation. Advances in Water Resources 2009, 32:1711-1716.
    • (2009) Advances in Water Resources , vol.32 , pp. 1711-1716
    • Yildirim, A.1    Kocak, H.2
  • 11
    • 19944370478 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional advection-dispersion equation
    • Huang F., Liu F. The fundamental solution of the space-time fractional advection-dispersion equation. Journal of Applied Mathematics and Computing 2005, 18:339-350.
    • (2005) Journal of Applied Mathematics and Computing , vol.18 , pp. 339-350
    • Huang, F.1    Liu, F.2
  • 12
    • 0000206373 scopus 로고    scopus 로고
    • Application of the Hirota bilinear formalism to a new integrable differential-difference equation
    • Hu X.B., Wu Y.T. Application of the Hirota bilinear formalism to a new integrable differential-difference equation. Physics Letters A 1998, 246:523-529.
    • (1998) Physics Letters A , vol.246 , pp. 523-529
    • Hu, X.B.1    Wu, Y.T.2
  • 14
    • 0001402844 scopus 로고    scopus 로고
    • Two applications of the homogeneous balance method
    • Fan E. Two applications of the homogeneous balance method. Physics Letters A 2000, 256:353-357.
    • (2000) Physics Letters A , vol.256 , pp. 353-357
    • Fan, E.1
  • 15
    • 0037411678 scopus 로고    scopus 로고
    • A Bäcklund transformation and their inverse scatting transform method for the generalized Vakhnenko equation
    • Vakhnenko V.O., Parkes E.J., Morrision A.J. A Bäcklund transformation and their inverse scatting transform method for the generalized Vakhnenko equation. Chaos, Solitons and Fractals 2003, 17:683-692.
    • (2003) Chaos, Solitons and Fractals , vol.17 , pp. 683-692
    • Vakhnenko, V.O.1    Parkes, E.J.2    Morrision, A.J.3
  • 16
    • 55549139469 scopus 로고    scopus 로고
    • Analysis of nonlinear fractional partial differential equations with the homotopy analysis method
    • Xu H., Liao S.J., You X.C. Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. Communications in Nonlinear Science and Numerical Simulation 2009, 14:1152-1156.
    • (2009) Communications in Nonlinear Science and Numerical Simulation , vol.14 , pp. 1152-1156
    • Xu, H.1    Liao, S.J.2    You, X.C.3
  • 17
    • 34250668369 scopus 로고    scopus 로고
    • Variational iteration method-Some recent results and new interpretations
    • He J.H. Variational iteration method-Some recent results and new interpretations. Journal of Computational and Applied Mathematics 2007, 207(1):3-17.
    • (2007) Journal of Computational and Applied Mathematics , vol.207 , Issue.1 , pp. 3-17
    • He, J.H.1
  • 19
    • 39449122795 scopus 로고    scopus 로고
    • Generalized differential transform method: application to differential equations of fractional order
    • Odibat Z., Momani S., Erturk V.S. Generalized differential transform method: application to differential equations of fractional order. Applied Mathematics and Computation 2008, 197:467-477.
    • (2008) Applied Mathematics and Computation , vol.197 , pp. 467-477
    • Odibat, Z.1    Momani, S.2    Erturk, V.S.3
  • 21
    • 79951959074 scopus 로고    scopus 로고
    • A study on the multi-order time fractional differential equations with using homotopy perturbation method
    • Golbabai A., Sayevand K. A study on the multi-order time fractional differential equations with using homotopy perturbation method. Nonlinear Science Letters A 2010, 2:141-147.
    • (2010) Nonlinear Science Letters A , vol.2 , pp. 141-147
    • Golbabai, A.1    Sayevand, K.2
  • 22
    • 67349159410 scopus 로고    scopus 로고
    • Modified homotopy perturbation method for solving system of linear Fredholm integral equations
    • Javidi M. Modified homotopy perturbation method for solving system of linear Fredholm integral equations. Mathematical and Computer Modelling 2009, 50:159-165.
    • (2009) Mathematical and Computer Modelling , vol.50 , pp. 159-165
    • Javidi, M.1
  • 23
    • 67349144675 scopus 로고    scopus 로고
    • Fourth-order and fifth-order iterative methods for nonlinear algebraic equations
    • Javidi M. Fourth-order and fifth-order iterative methods for nonlinear algebraic equations. Mathematical and Computer Modelling 2009, 50:66-71.
    • (2009) Mathematical and Computer Modelling , vol.50 , pp. 66-71
    • Javidi, M.1
  • 24
    • 67249166170 scopus 로고    scopus 로고
    • An algorithm for solving the fractional nonlinear Schördinger equation by means of the homotopy perturbation method
    • Yildirim A. An algorithm for solving the fractional nonlinear Schördinger equation by means of the homotopy perturbation method. International Journal of Nonlinear Sciences and Numerical Simulation 2009, 10:445-450.
    • (2009) International Journal of Nonlinear Sciences and Numerical Simulation , vol.10 , pp. 445-450
    • Yildirim, A.1
  • 25
    • 77955858024 scopus 로고    scopus 로고
    • A note on the homotopy perturbation method
    • He J.H. A note on the homotopy perturbation method. Thermal Science 2010, 14(2):565-568.
    • (2010) Thermal Science , vol.14 , Issue.2 , pp. 565-568
    • He, J.H.1
  • 26
    • 33745742268 scopus 로고    scopus 로고
    • Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results
    • Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions further results. Computers and Mathematics with Applications 2006, 51:1367-1376.
    • (2006) Computers and Mathematics with Applications , vol.51 , pp. 1367-1376
    • Jumarie, G.1
  • 27
    • 57049186538 scopus 로고    scopus 로고
    • Table of some basic fractional calculus formulate derived from a modified Riemann-Liouville derivative for non-differentiable functions
    • Jumarie G. Table of some basic fractional calculus formulate derived from a modified Riemann-Liouville derivative for non-differentiable functions. Applied Mathematics Letters 2009, 22:378-385.
    • (2009) Applied Mathematics Letters , vol.22 , pp. 378-385
    • Jumarie, G.1
  • 28
    • 77953478412 scopus 로고    scopus 로고
    • Fractional calculus of variations in fractal space time
    • Wu G.C., He J.H. Fractional calculus of variations in fractal space time. Nonlinear Science Letters A 2010, 1:281-287.
    • (2010) Nonlinear Science Letters A , vol.1 , pp. 281-287
    • Wu, G.C.1    He, J.H.2
  • 29
    • 77953478991 scopus 로고    scopus 로고
    • Fractional variational iteration method and its application
    • Wu G.C., Lee E.W.M. Fractional variational iteration method and its application. Physics Letters A 2010, 374:2506-2509.
    • (2010) Physics Letters A , vol.374 , pp. 2506-2509
    • Wu, G.C.1    Lee, E.W.M.2
  • 30
    • 82955223413 scopus 로고    scopus 로고
    • Fractional variational iteration method via modified Riemann-Liouville derivative. doi:10.1016/j.jksus.2010.07.025
    • N. Faraz, Y. Khan, H. Jafari, M. Madani, Fractional variational iteration method via modified Riemann-Liouville derivative. doi:10.1016/j.jksus.2010.07.025.
    • Faraz, N.1    Khan, Y.2    Jafari, H.3    Madani, M.4
  • 32
    • 55649102766 scopus 로고    scopus 로고
    • Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part
    • Hosseinnia S.H., Ranjbar A., Momani S. Using an enhanced homotopy perturbation method in fractional differential equations via deforming the linear part. Computer and Mathematics with Applications 2008, 56:3138-3149.
    • (2008) Computer and Mathematics with Applications , vol.56 , pp. 3138-3149
    • Hosseinnia, S.H.1    Ranjbar, A.2    Momani, S.3
  • 33
    • 64449088045 scopus 로고    scopus 로고
    • Convergence of the homotopy perturbation method for partial differential equation
    • Biazar J., Ghazvini H. Convergence of the homotopy perturbation method for partial differential equation. NonLinear Analysis: Real World Application 2009, 10:2633-2640.
    • (2009) NonLinear Analysis: Real World Application , vol.10 , pp. 2633-2640
    • Biazar, J.1    Ghazvini, H.2
  • 34
    • 0347450513 scopus 로고    scopus 로고
    • A new algorithm for calculating Adomian polynomials for nonlinear operator
    • Wazwaz A. A new algorithm for calculating Adomian polynomials for nonlinear operator. Applied Mathematics and Computation 2000, 111:53-69.
    • (2000) Applied Mathematics and Computation , vol.111 , pp. 53-69
    • Wazwaz, A.1
  • 35
    • 55349110254 scopus 로고    scopus 로고
    • Response and stability of a SDOF strongly nonlinear stochastic system with high damping modeled by a fractional derivative
    • Huang Z.L., Jin X.L. Response and stability of a SDOF strongly nonlinear stochastic system with high damping modeled by a fractional derivative. Journal of Sound and Vibration 2009, 319:1121-1135.
    • (2009) Journal of Sound and Vibration , vol.319 , pp. 1121-1135
    • Huang, Z.L.1    Jin, X.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.