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Volumn 235, Issue 10, 2011, Pages 3121-3137

Numerical method for solving diffusion-wave phenomena

Author keywords

Approximation of tempered convolution; Convolution equations; Diffusion wave phenomena; Fractional equations of distributed order; Laguerre polynomials; Tempered distributions

Indexed keywords

APPROXIMATION OF TEMPERED CONVOLUTION; CONVOLUTION EQUATIONS; FRACTIONAL EQUATION; LAGUERRE POLYNOMIALS; TEMPERED DISTRIBUTIONS;

EID: 79952190735     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.12.010     Document Type: Article
Times cited : (28)

References (30)
  • 1
    • 41349088572 scopus 로고    scopus 로고
    • Retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations
    • A.V. Chechkin, R. Gorenflo, and I.M. Sokolov Retarding subdiffusion and accelerating superdiffusion governed by distributed order fractional diffusion equations Phys. Rev. E 66 2002 046129/17
    • (2002) Phys. Rev. e , vol.66
    • Chechkin, A.V.1    Gorenflo, R.2    Sokolov, I.M.3
  • 3
    • 49549105572 scopus 로고    scopus 로고
    • Generalized fractional diffusion equations for accelerating subdiffusion and truncated Levy flights
    • A.V. Chechkin, V.Yu. Gonchar, R. Gorenflo, N. Korabel, and I.M. Sokolov Generalized fractional diffusion equations for accelerating subdiffusion and truncated Levy flights Phys. Rev. E 78 2008 021111
    • (2008) Phys. Rev. e , vol.78 , pp. 021111
    • Chechkin, A.V.1    Gonchar, V.Yu.2    Gorenflo, R.3    Korabel, N.4    Sokolov, I.M.5
  • 4
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, and J. Klafter The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 2000 1 77
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 6
    • 1642617462 scopus 로고    scopus 로고
    • Fractional diffusion equation for a power-law-truncated Levy process
    • I.M. Sokolov, A.V. Checkin, and J. Klafter Fractional diffusion equation for a power-law-truncated Levy process Physica A 336 2004 245
    • (2004) Physica A , vol.336 , pp. 245
    • Sokolov, I.M.1    Checkin, A.V.2    Klafter, J.3
  • 7
    • 0041361963 scopus 로고    scopus 로고
    • Fractional FokkerPlanck equation for ultraslow kinetic
    • A.V. Checkin, J. Klafter, and I.M. Sokolov Fractional FokkerPlanck equation for ultraslow kinetic Europhys. Lett. 63 2003 326
    • (2003) Europhys. Lett. , vol.63 , pp. 326
    • Checkin, A.V.1    Klafter, J.2    Sokolov, I.M.3
  • 8
    • 31144434675 scopus 로고    scopus 로고
    • From diffusion to anomalous diffusion: A century after Einstein's Brownian motion
    • 101063/11860472
    • I.M. Sokolov, and J. Klafter From diffusion to anomalous diffusion: a century after Einstein's Brownian motion Chaos 15 2005 026103 10.1063/1.1860472
    • (2005) Chaos , vol.15 , pp. 026103
    • Sokolov, I.M.1    Klafter, J.2
  • 9
    • 32044453310 scopus 로고    scopus 로고
    • Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations, Part one
    • S. Umarov, and R. Gorenflo Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations part one J. Anal. Appl. 245 3 2005 449 466 (Pubitemid 43198318)
    • (2005) Zeitschrift fur Analysis und ihre Anwendung , vol.24 , Issue.3 , pp. 449-466
    • Umarov, S.1    Gorenflo, R.2
  • 10
    • 37449011239 scopus 로고    scopus 로고
    • Distributed order calculus and equations of ultraslow diffusion
    • A.N. Kochubei Distributed order calculus and equations of ultraslow diffusion J. Math. Anal. Appl. 340 1 2008 252 281
    • (2008) J. Math. Anal. Appl. , vol.340 , Issue.1 , pp. 252-281
    • Kochubei, A.N.1
  • 11
    • 0041025417 scopus 로고
    • Parabolic pseudodifferential equations, hypersingular integrals and Markov processes
    • A.N. Kochubei Parabolic pseudodifferential equations, hypersingular integrals and Markov processes Math. USSR Izv. 33 1989 233 259
    • (1989) Math. USSR Izv. , vol.33 , pp. 233-259
    • Kochubei, A.N.1
  • 12
    • 0013118687 scopus 로고
    • Pseudodifferential operators with variable order of differentiation generating Feller semigroups
    • N. Jacob, and H.-G. Leopold Pseudodifferential operators with variable order of differentiation generating Feller semigroups Integral Equations Operator Theory 17 1993 544 553
    • (1993) Integral Equations Operator Theory , vol.17 , pp. 544-553
    • Jacob, N.1    Leopold, H.-G.2
  • 13
    • 0141996364 scopus 로고    scopus 로고
    • Fully discrete random walks for spacetime fractional diffusion equations
    • R. Gorenflo, and A. Vivoli Fully discrete random walks for spacetime fractional diffusion equations Signal Process. 83 2003 2411 2420
    • (2003) Signal Process. , vol.83 , pp. 2411-2420
    • Gorenflo, R.1    Vivoli, A.2
  • 14
    • 79952195640 scopus 로고    scopus 로고
    • Fractal derivative modelling of anomalous diffusion
    • Ankara, 5-7 November
    • W. Chen, H. Sun, X. Zhang, L. Ye, Fractal derivative modelling of anomalous diffusion, in: Proc. Symp. FDA08, Ankara, 57 November, 2008.
    • (2008) Proc. Symp. FDA08
    • Chen, W.1    Sun, H.2    Zhang, X.3    Ye, L.4
  • 15
    • 33845224721 scopus 로고
    • Solving convolution equations in S+′ by numerical method
    • S. Pilipovi, and M. Stojanovi Solving convolution equations in S + ′ by numerical method Publ. Math. Debrecen 40 12 1992 17 33
    • (1992) Publ. Math. Debrecen , vol.40 , Issue.12 , pp. 17-33
    • Pilipovi, S.1    Stojanovi, M.2
  • 16
    • 33845193177 scopus 로고    scopus 로고
    • Fractional differential equations through Laguerre expansions in abstract spaces. Error estimates
    • S. Pilipovi, and M. Stojanovi Fractional differential equations through Laguerre expansions in abstract spaces. Error estimates Integral Transforms Spec. Funct. 17 12 2006 877 887
    • (2006) Integral Transforms Spec. Funct. , vol.17 , Issue.12 , pp. 877-887
    • Pilipovi, S.1    Stojanovi, M.2
  • 18
    • 77952835494 scopus 로고    scopus 로고
    • On the convolution equations over the quarter-plane
    • M. Stojanovi On the convolution equations over the quarter-plane Novi Sad J. Math. 26 2 1996 127 149
    • (1996) Novi Sad J. Math. , vol.26 , Issue.2 , pp. 127-149
    • Stojanovi, M.1
  • 19
    • 0002847893 scopus 로고    scopus 로고
    • Fractional calculus, integral and integrodifferential equations of fractional order
    • R. Gorenflo, and F. Mainardi Fractional calculus, integral and integrodifferential equations of fractional order A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer Wien 223 276
    • (1997) Fractals and Fractional Calculus in Continuum Mechanics , pp. 223-276
    • Gorenflo, R.1    Mainardi, F.2
  • 20
    • 0025451323 scopus 로고
    • Laguerre expansions of tempered distributions and generalized functions
    • A.J. Duran Laguerre expansions of tempered distributions and generalized functions J. Math. Anal. Appl. 150 1990 166 180
    • (1990) J. Math. Anal. Appl. , vol.150 , pp. 166-180
    • Duran, A.J.1
  • 21
    • 0011277353 scopus 로고
    • On the Laguerre expansions of generalized functions
    • S. Pilipovi On the Laguerre expansions of generalized functions C. R. Math. 1 1989 23 27
    • (1989) C. R. Math. , vol.1 , pp. 23-27
    • Pilipovi, S.1
  • 22
    • 2442628845 scopus 로고
    • Generalization of Zemanian spaces of generalized functions which have orthogonal series expansions
    • S. Pilipovi Generalization of Zemanian spaces of generalized functions which have orthogonal series expansions SIAM J. Math. Anal. 17 1986 477 484
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 477-484
    • Pilipovi, S.1
  • 23
    • 22544483915 scopus 로고    scopus 로고
    • Volterra-type equations in the space S+′
    • S. Pilipovi, and M. Stojanovi Volterra-type equations in the space S + ′ Mat. Zametki 75 1 2004 135 141 (in Russian); translation in Math. Notes 75 (12) (2004) 124130
    • (2004) Mat. Zametki , vol.75 , Issue.1 , pp. 135-141
    • Pilipovi, S.1    Stojanovi, M.2
  • 24
    • 33845202402 scopus 로고    scopus 로고
    • Splitting S+′ space into union of Banach spaces through the Laguerre expansions
    • M. Stojanovi Splitting S + ′ space into union of Banach spaces through the Laguerre expansions Comput. Methods Appl. Math. 6 3 2006 1 9
    • (2006) Comput. Methods Appl. Math. , vol.6 , Issue.3 , pp. 1-9
    • Stojanovi, M.1
  • 28
    • 0011270142 scopus 로고
    • Laguerre series as boundary values
    • A. Zayed Laguerre series as boundary values SIAM J. Math. Anal. 13 1982 263 279
    • (1982) SIAM J. Math. Anal. , vol.13 , pp. 263-279
    • Zayed, A.1
  • 30
    • 58149289694 scopus 로고    scopus 로고
    • Existence-uniqueness result for a nonlinear n-terms fractional equation
    • M. Stojanovi Existence-uniqueness result for a nonlinear n-terms fractional equation J. Math. Anal. Appl. 353 2009 244 255
    • (2009) J. Math. Anal. Appl. , vol.353 , pp. 244-255
    • Stojanovi, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.