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Volumn 14, Issue 4, 2013, Pages 287-292

Transport equations in fractal porous media within fractional complex transform method

Author keywords

Fractional complex transform method; Local fractional derivatives; Transport equations

Indexed keywords


EID: 84890267857     PISSN: 14549069     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (33)

References (59)
  • 2
    • 47049103034 scopus 로고    scopus 로고
    • Hierarchy of wool fibers and fractal dimensions
    • J. Fan, J. F. Liu, J.H. He, Hierarchy of wool fibers and fractal dimensions, Inter. J. Nonlin. Sci. Numer. Simul, 9, 3, pp. 293-296, 2008.
    • (2008) Inter. J. Nonlin. Sci. Numer. Simul , vol.9 , Issue.3 , pp. 293-296
    • Fan, J.1    Liu, J.F.2    He, J.H.3
  • 3
    • 84856100248 scopus 로고    scopus 로고
    • From spider spinning to bubble electrospinning and from the wool structure to carbon super-nanotubes
    • J. H. He, From spider spinning to bubble electrospinning and from the wool structure to carbon super-nanotubes, Mat. Sci. Tech., 26, 11, pp. 1273-1274, 2010.
    • (2010) Mat. Sci. Tech. , vol.26 , Issue.11 , pp. 1273-1274
    • He, J.H.1
  • 4
    • 84874783648 scopus 로고    scopus 로고
    • Biomimic design of multi-scale fabric with efficient heat transfer property
    • J. Fan, J. H. He, Biomimic design of multi-scale fabric with efficient heat transfer property, Ther. Sci., 16, 5, pp. 1349-1352, 2012.
    • (2012) Ther. Sci. , vol.16 , Issue.5 , pp. 1349-1352
    • Fan, J.1    He, J.H.2
  • 5
    • 84863370700 scopus 로고    scopus 로고
    • Fractional model for heat conduction in polar bear hairs
    • Q. L. Wang, J. H. He, Z. B. Li, Fractional model for heat conduction in polar bear hairs, Ther. Sci., 16, 2, pp. 339-342, 2012.
    • (2012) Ther. Sci. , vol.16 , Issue.2 , pp. 339-342
    • Wang, Q.L.1    He, J.H.2    Li, Z.B.3
  • 6
    • 84871448093 scopus 로고    scopus 로고
    • Fractal derivative model for air permeability in hierarchic porous media
    • J. Fan, J. H. He, Fractal derivative model for air permeability in hierarchic porous media, Abstr. Appl. Anal., 2012, 354701, 2012.
    • (2012) Abstr. Appl. Anal. , vol.2012 , pp. 354701
    • Fan, J.1    He, J.H.2
  • 7
    • 0030300846 scopus 로고    scopus 로고
    • Transports in fractal porous media
    • P. M. Adler, Transports in fractal porous media, J. Hydrol., 187, pp. 195-213, 1996.
    • (1996) J. Hydrol , vol.187 , pp. 195-213
    • Adler, P.M.1
  • 8
    • 36849100388 scopus 로고
    • Transport equations in turbulence
    • B. J. Daly, F. H. Harlow, Transport equations in turbulence, Phys. Fluids, 13, 11, 2634, 1970.
    • (1970) Phys. Fluids , vol.13 , Issue.11 , pp. 2634
    • Daly, B.J.1    Harlow, F.H.2
  • 9
    • 0014705867 scopus 로고
    • Transport equations for electrons in two-valley semiconductors
    • K. Blotekjaer, Transport equations for electrons in two-valley semiconductors, IEEE Transactions on Electron Devices, 17, 1, pp. 38-47, 1970.
    • (1970) IEEE Transactions on Electron Devices , vol.17 , Issue.1 , pp. 38-47
    • Blotekjaer, K.1
  • 10
    • 0009123541 scopus 로고
    • Transport equations for the QCD gluon Wigner operator
    • H. T. Elze, M. Gyulassy, D. Vasak, Transport equations for the QCD gluon Wigner operator, Phys. Lett. B, 177, pp. 402-408, 1986.
    • (1986) Phys. Lett. B , vol.177 , pp. 402-408
    • Elze, H.T.1    Gyulassy, M.2    Vasak, D.3
  • 11
    • 2342648426 scopus 로고
    • Transport equations in clean superconductors
    • O. Betbeder-Matibet, P. Nozieres, Transport equations in clean superconductors, Ann. Phys., 51, 3, pp. 392-417. 1969.
    • (1969) Ann. Phys. , vol.51 , Issue.3 , pp. 392-417
    • Betbeder-Matibet, O.1    Nozieres, P.2
  • 12
    • 0001761745 scopus 로고
    • Transport equations for aeronomy
    • R. W. Schunk, Transport equations for aeronomy, Planet. Space Sci., 23, 3, pp. 437-485, 1975.
    • (1975) Planet. Space Sci. , vol.23 , Issue.3 , pp. 437-485
    • Schunk, R.W.1
  • 13
    • 4243764521 scopus 로고
    • Transport equations for superconductors
    • M. J. Stephen, Transport equations for superconductors, Phys. Rev., 139, pp. A197-A205, 1965.
    • (1965) Phys. Rev. , vol.139 , pp. 197-205
    • Stephen, M.J.1
  • 14
    • 0242710950 scopus 로고    scopus 로고
    • Transport equations with resting phases
    • T. Hillen, Transport equations with resting phases, Eur. J. Appl. Math., 14, 5, pp. 613-636, 2003.
    • (2003) Eur. J. Appl. Math. , vol.14 , Issue.5 , pp. 613-636
    • Hillen, T.1
  • 18
    • 84875677289 scopus 로고    scopus 로고
    • Fractional Caputo heat equation with the double Laplace transform
    • A. M. O. Anwar, F. Jarad, D. Baleanu, F. Ayazi, Fractional Caputo heat equation with the double Laplace transform, Rom. J. Phys., 58, pp. 15-22, 2013;
    • (2013) Rom. J. Phys. , vol.58 , pp. 15-22
    • Anwar, A.M.O.1    Jarad, F.2    Baleanu, D.3    Ayazi, F.4
  • 19
    • 79959998825 scopus 로고    scopus 로고
    • On fractional coupled Whitham-Broer-Kaup equations
    • A. Kadem, D. Baleanu, On fractional coupled Whitham-Broer-Kaup equations, Rom. J. Phys., 56, pp. 629-635, 2011;
    • (2011) Rom. J. Phys. , vol.56 , pp. 629-635
    • Kadem, A.1    Baleanu, D.2
  • 20
    • 79960028808 scopus 로고    scopus 로고
    • Lyapunov-Krasovskii stability theorem for fractional systems with delay
    • D. Baleanu et al., Lyapunov-Krasovskii stability theorem for fractional systems with delay, Rom. J. Phys., 56, pp. 636-643, 2011;
    • (2011) Rom. J. Phys. , vol.56 , pp. 636-643
    • Baleanu, D.1
  • 21
    • 84877833378 scopus 로고    scopus 로고
    • Fractional calculus analysis of the cosmic microwave background
    • J.A. Tenreiro Machado et al., Fractional calculus analysis of the cosmic microwave background, Rom. Rep. Phys., 65, pp. 316-323, 2013.
    • (2013) Rom. Rep. Phys. , vol.65 , pp. 316-323
    • Machado, J.A.T.1
  • 22
    • 84879528675 scopus 로고    scopus 로고
    • Fractional Euler-Lagrange equation of Caldirola-Kanai oscillator
    • D. Baleanu, J. H. Asad, I. Petras, S. Elagan, A. Bilgen, Fractional Euler-Lagrange equation of Caldirola-Kanai oscillator, Rom. Rep. Phys., 64, pp.1171-1177, 2012;
    • (2012) Rom. Rep. Phys. , vol.64 , pp. 1171-1177
    • Baleanu, D.1    Asad, J.H.2    Petras, I.3    Elagan, S.4    Bilgen, A.5
  • 23
    • 84869470751 scopus 로고    scopus 로고
    • Fractional-order two-electric pendulum
    • D. Baleanu, J. H. Asad, I. Petras, Fractional-order two-electric pendulum, Rom. Rep. Phys., 64, pp. 907-914, 2012;
    • (2012) Rom. Rep. Phys. , vol.64 , pp. 907-991
    • Baleanu, D.1    Asad, J.H.2    Petras, I.3
  • 24
    • 79953886340 scopus 로고    scopus 로고
    • On fractional Hamiltonian systems possessing first-class constraints within Caputo derivatives
    • D. Baleanu et al., On fractional Hamiltonian systems possessing first-class constraints within Caputo derivatives, Rom. Rep. Phys., 63, pp. 3-8, 2011;
    • (2011) Rom. Rep. Phys. , vol.63 , pp. 3-8
    • Baleanu, D.1
  • 26
    • 84877806817 scopus 로고    scopus 로고
    • Newtonian mechanics on fractals subset of real-line
    • A.K. Golmankhaneh et al., Newtonian mechanics on fractals subset of real-line, Rom. Rep. Phys., 65, pp. 84-93, 2013.
    • (2013) Rom. Rep. Phys. , vol.65 , pp. 84-93
    • Golmankhaneh, A.K.1
  • 27
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • G. M. Zaslavsky, Chaos, fractional kinetics, and anomalous transport, Phys. Rep., 371, 6, pp. 461-580, 2002.
    • (2002) Phys. Rep. , vol.371 , Issue.6 , pp. 461-580
    • Zaslavsky, G.M.1
  • 28
    • 0001536558 scopus 로고    scopus 로고
    • Anomalous transport in external fields: Continuous time random walks and fractional diffusion equations extended
    • R. Metzler, J. Klafter, I. M. Sokolov, Anomalous transport in external fields: Continuous time random walks and fractional diffusion equations extended, Phys. Rev. E, 58, pp. 1621-1633, 1998.
    • (1998) Phys. Rev. e , vol.58 , pp. 1621-1633
    • Metzler, R.1    Klafter, J.2    Sokolov, I.M.3
  • 29
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Phys. Rep., 339, pp. 1-77, 2000.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 30
    • 41349112464 scopus 로고    scopus 로고
    • Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: Application to the theory of Neolithic transition
    • M. O. Vlad, J. Ross, Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: Application to the theory of Neolithic transition, Phys. Rev. E, 66, 061908, 2002.
    • (2002) Phys. Rev. e , vol.66 , pp. 061908
    • Vlad, M.O.1    Ross, J.2
  • 31
    • 33748295799 scopus 로고    scopus 로고
    • Fractional diffusion models of nonlocal transport
    • D. Del-Castillo-Negrete, Fractional diffusion models of nonlocal transport, Phys. Plasma, 13, 082308, 2006.
    • (2006) Phys. Plasma , vol.13 , pp. 082308
    • Del-Castillo-Negrete, D.1
  • 32
    • 35548973459 scopus 로고    scopus 로고
    • Fractional theory for transport in disordered semiconductors
    • V. V. Uchaikin, R. T. Sibatov, Fractional theory for transport in disordered semiconductors, Comm. Nonlin. Sci. Numer. Simul., 13, 4, pp. 715-727, 2008.
    • (2008) Comm. Nonlin. Sci. Numer. Simul. , vol.13 , Issue.4 , pp. 715-727
    • Uchaikin, V.V.1    Sibatov, R.T.2
  • 33
    • 70349986628 scopus 로고    scopus 로고
    • Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation
    • A. Kadem, D. Baleanu, Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation, Comm. Nonlin. Sci. Numer. Simul., 15, 3, pp. 491-501, 2010.
    • (2010) Comm. Nonlin. Sci. Numer. Simul. , vol.15 , Issue.3 , pp. 491-501
    • Kadem, A.1    Baleanu, D.2
  • 34
    • 79952536080 scopus 로고    scopus 로고
    • Solution of a fractional transport equation by using the generalized quadratic form
    • A. Kadem, D. Baleanu, Solution of a fractional transport equation by using the generalized quadratic form, Comm. Nonlin. Sci. Numer. Simul., 16, 8, pp. 3011-3014, 2011.
    • (2011) Comm. Nonlin. Sci. Numer. Simul. , vol.16 , Issue.8 , pp. 3011-3014
    • Kadem, A.1    Baleanu, D.2
  • 37
    • 0040655648 scopus 로고    scopus 로고
    • Fractional differentiability of nowhere differentiable functions and dimensions
    • K. M. Kolwankar, A. D. Gangal, Fractional differentiability of nowhere differentiable functions and dimensions, Chaos, 6, 4, pp. 505-513, 1996.
    • (1996) Chaos , vol.6 , Issue.4 , pp. 505-513
    • Kolwankar, K.M.1    Gangal, A.D.2
  • 38
    • 78649351641 scopus 로고    scopus 로고
    • Investigation on fractional and fractal derivative relaxation- oscillation models
    • W. Chen, X. D. Zhang, D. Korosak, Investigation on fractional and fractal derivative relaxation- oscillation models, Inter. J. Nonlin. Sci. Numer. Simul., 11, pp. 3-9, 2010.
    • (2010) Inter. J. Nonlin. Sci. Numer. Simul. , vol.11 , pp. 3-9
    • Chen, W.1    Zhang, X.D.2    Korosak, D.3
  • 39
    • 33745108563 scopus 로고    scopus 로고
    • Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order
    • G. Jumarie, Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order, Appl. Math. Lett., 19, pp. 873-880, 2006.
    • (2006) Appl. Math. Lett. , vol.19 , pp. 873-880
    • Jumarie, G.1
  • 40
    • 79955145165 scopus 로고    scopus 로고
    • A new fractal derivation
    • J. H. He, A new fractal derivation, Ther. Sci., 15, pp. S145-S147, 2011.
    • (2011) Ther. Sci. , vol.15 , pp. 145-147
    • He, J.H.1
  • 41
    • 84874182595 scopus 로고    scopus 로고
    • One-phase problems for discontinuous heat transfer in fractal media
    • M. S. Hu, D. Baleanu, X. J. Yang, One-phase problems for discontinuous heat transfer in fractal media, Math. Probl. Eng., 2013, 358473, 2013.
    • (2013) Math. Probl. Eng. , vol.2013 , pp. 358473
    • Hu, M.S.1    Baleanu, D.2    Yang, X.J.3
  • 42
    • 84874162681 scopus 로고    scopus 로고
    • The zero-mass renormalization group differential equations and limit cycles in non-smooth initial value problems
    • X. J. Yang, The zero-mass renormalization group differential equations and limit cycles in non-smooth initial value problems, Prespacetime J., 3, 9, pp. 913-923, 2012.
    • (2012) Prespacetime J. , vol.3 , Issue.9 , pp. 913-923
    • Yang, X.J.1
  • 43
    • 84879324154 scopus 로고    scopus 로고
    • Fractal heat conduction problem solved by local fractional variation iteration method
    • Doi: 10.2298/TSCI121124216Y
    • X. J. Yang, D. Baleanu, Fractal heat conduction problem solved by local fractional variation iteration method, Ther. Sci., 2012, Doi: 10.2298/TSCI121124216Y.
    • (2012) Ther. Sci.
    • Yang, X.J.1    Baleanu, D.2
  • 44
    • 84878993985 scopus 로고    scopus 로고
    • Approximation solutions for diffusion equation on cantor time-space
    • Xiao-Jun Yang, D. Baleanu, W. P. , Approximation solutions for diffusion equation on Cantor time-space, Proc. Romanian Acad. A, 14, pp. 127-133, 2013.
    • (2013) Proc. Romanian Acad. A , vol.14 , pp. 127-133
    • Yang, X.-J.1    Baleanu, D.2    Zhong, W.P.3
  • 45
    • 84872148874 scopus 로고    scopus 로고
    • Local fractional Fourier series with application to wave equation in fractal vibrating string
    • M. S. Hu, R. P. Agarwal, X. J. Yang, Local fractional Fourier series with application to wave equation in fractal vibrating string, Abstr. Appl. Anal., 2012, 567401, 2012.
    • (2012) Abstr. Appl. Anal. , vol.2012 , pp. 567401
    • Hu, M.S.1    Agarwal, R.P.2    Yang, X.J.3
  • 47
    • 84857467321 scopus 로고    scopus 로고
    • Applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral
    • W. P. Zhong, F. Gao, X. M. Shen, Applications of Yang-Fourier transform to local fractional equations with local fractional derivative and local fractional integral, Adv. Mat. Res., 461, pp. 306-310, 2012.
    • (2012) Adv. Mat. Res. , vol.461 , pp. 306-310
    • Zhong, W.P.1    Gao, F.2    Shen, X.M.3
  • 48
    • 84869494625 scopus 로고    scopus 로고
    • Asymptotic methods for solitary solutions and compactons
    • J. H. He, Asymptotic methods for solitary solutions and compactons, Abstr. Appl. Anal., 2012, 916793, 2012.
    • (2012) Abstr. Appl. Anal. , vol.2012 , pp. 916793
    • He, J.H.1
  • 49
    • 79955470495 scopus 로고    scopus 로고
    • Fractional complex transform for fractional differential equations
    • Z. B. Li, J. H. He, Fractional complex transform for fractional differential equations, Math. Comput. Appl., 15, 5, pp. 970-973, 2010.
    • (2010) Math. Comput. Appl. , vol.15 , Issue.5 , pp. 970-973
    • Li, Z.B.1    He, J.H.2
  • 50
    • 84868613849 scopus 로고    scopus 로고
    • Converting fractional differential equations into partial differential equations
    • J. H. He, Z. B. Li, Converting fractional differential equations into partial differential equations, Ther. Sci., 16, 2, pp. 331-334, 2012.
    • (2012) Ther. Sci. , vol.16 , Issue.2 , pp. 331-334
    • He, J.H.1    Li, Z.B.2
  • 51
    • 80051855070 scopus 로고    scopus 로고
    • An extended fractional complex transform
    • Z. B. Li, An extended fractional complex transform, J. Non. Sci. Num. Simul., 11, pp. 335-337, 2010.
    • (2010) J. Non. Sci. Num. Simul , vol.11 , pp. 335-337
    • Li, Z.B.1
  • 52
    • 84860388823 scopus 로고    scopus 로고
    • A short remark on fractional variational iteration method
    • J. H. He, A short remark on fractional variational iteration method, Phys. Lett. A, 375, 38, pp. 3362-3364, 2011.
    • (2011) Phys. Lett. A , vol.375 , Issue.38 , pp. 3362-3364
    • He, J.H.1
  • 53
    • 80051828842 scopus 로고    scopus 로고
    • Application of the fractional complex transform to fractional differential equations
    • Z. B. Li, J.H. He, Application of the fractional complex transform to fractional differential equations, Nonlin. Sci. Letters A, 2, 3, pp. 121-126, 2011.
    • (2011) Nonlin. Sci. Letters A , vol.2 , Issue.3 , pp. 121-126
    • Li, Z.B.1    He, J.H.2
  • 54
    • 84868609962 scopus 로고    scopus 로고
    • Exact solutions of time-fractional heat conduction equation by the fractional complex transform
    • Z. B. Li, W. H. Zhu, J. H. He, Exact solutions of time-fractional heat conduction equation by the fractional complex transform, Ther. Sci., 16, 2, pp. 335-338, 2012.
    • (2012) Ther. Sci. , vol.16 , Issue.2 , pp. 335-338
    • Li, Z.B.1    Zhu, W.H.2    He, J.H.3
  • 55
    • 84855203771 scopus 로고    scopus 로고
    • Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus
    • J. H. He, S. K. Elagan, Z. B. Li, Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus, Phys. Lett. A, 376, 4, pp. 257-259, 2012.
    • (2012) Phys. Lett. A , vol.376 , Issue.4 , pp. 257-259
    • He, J.H.1    Elagan, S.K.2    Li, Z.B.3
  • 56
    • 84871847812 scopus 로고    scopus 로고
    • Complex transforms for systems of fractional differential equations
    • R. W. Ibrahim, Complex transforms for systems of fractional differential equations, Abstr. Appl. Anal., 2012, 814759, 2012.
    • (2012) Abstr. Appl. Anal. , vol.2012 , pp. 814759
    • Ibrahim, R.W.1
  • 57
    • 84861498408 scopus 로고    scopus 로고
    • Solving system of fractional differential equations by fractional complex transform method
    • DOI: 10.3923/ajaps.2012
    • B. Ghazanfari, A. G. Ghazanfari, Solving system of fractional differential equations by fractional complex transform method, Asian J. Appl. Sci., DOI: 10.3923/ajaps.2012.
    • Asian J. Appl. Sci.
    • Ghazanfari, B.1    Ghazanfari, A.G.2
  • 58
    • 0010996358 scopus 로고    scopus 로고
    • On two-dimensional Hamiltonian transport equations with continuous coefficients
    • F. Bouchut, L. Desvillettes, On two-dimensional Hamiltonian transport equations with continuous coefficients, Diff. Integral Eqs., 14, 8, pp.1015-1024, 2001.
    • (2001) Diff. Integral Eqs. , vol.14 , Issue.8 , pp. 1015-1024
    • Bouchut, F.1    Desvillettes, L.2
  • 59
    • 77949722263 scopus 로고    scopus 로고
    • Reduced basis method for quadratically nonlinear transport equations
    • N. Jung, B. Haasdonk, D. Kroner, Reduced basis method for quadratically nonlinear transport equations, Inter. J. Comput. Sci. Math., 2, 4, pp. 334-353, 2009.
    • (2009) Inter. J. Comput. Sci. Math. , vol.2 , Issue.4 , pp. 334-353
    • Jung, N.1    Haasdonk, B.2    Kroner, D.3


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