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Volumn 50, Issue 1, 2009, Pages 45-57

The fundamental and numerical solutions of the Riesz space-fractional reaction-dispersion equation

Author keywords

convergence; fractional derivatives; probability density; random walk; stability

Indexed keywords


EID: 77954685875     PISSN: 14461811     EISSN: 14468735     Source Type: Journal    
DOI: 10.1017/S1446181108000333     Document Type: Article
Times cited : (24)

References (25)
  • 5
    • 0000103589 scopus 로고    scopus 로고
    • Wright function as scale-invariant solutions of the diffusion-wave equation"
    • R. Gorenflo, Yu. Luchko and F. Mainardi, "Wright function as scale-invariant solutions of the diffusion-wave equation", J. Comput. Appl. Math. 118 (2000) 175-191.
    • (2000) J. Comput. Appl. Math. , vol.118 , pp. 175-191
    • Gorenflo, R.1    Luchko, Yu.2    Mainardi, F.3
  • 6
    • 0000361678 scopus 로고    scopus 로고
    • Random walk models for space-fractional diffusion processes
    • R. Gorenflo and F. Mainardi, "Random walk models for space-fractional diffusion processes", Fract. Calc. Appl. Anal. 1 (1998) 167-191.
    • (1998) Fract. Calc. Appl. Anal. , vol.1 , pp. 167-191
    • Gorenflo, R.1    Mainardi, F.2
  • 7
    • 0345725412 scopus 로고    scopus 로고
    • Approximation of Lévy-Feller diffusion by random walk
    • R. Gorenflo and F. Mainardi, "Approximation of Lévy-Feller diffusion by random walk", Z Anal. Anwendungen 18 (1999) 231-246.
    • (1999) Z Anal. Anwendungen , vol.18 , pp. 231-246
    • Gorenflo, R.1    Mainardi, F.2
  • 8
    • 0036306866 scopus 로고    scopus 로고
    • Existence of Turing instabilities in a two-species fractional reaction-diffusion system
    • B. I. Henry and S. L. Wearne, "Existence of Turing instabilities in a two-species fractional reaction-diffusion system", SIAM J. Appl. Math. 62 (2002) 870-887.
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 870-887
    • Henry, B.I.1    Wearne, S.L.2
  • 10
    • 33751545053 scopus 로고    scopus 로고
    • Fractional high order methods for the nonlinear fractional ordinary differential equation
    • R. Lin and F. Liu, "Fractional high order methods for the nonlinear fractional ordinary differential equation", Nonlinear Anal. 66 (2007) 856-869.
    • (2007) Nonlinear Anal. , vol.66 , pp. 856-869
    • Lin, R.1    Liu, F.2
  • 12
    • 1542425102 scopus 로고    scopus 로고
    • Numerical solution of space-fractional Fokker-Planck equation
    • F. Liu, V. Ann and I. Turner, "Numerical solution of space-fractional Fokker-Planck equation", J. Comput. Appl. Math. 166 (2004) 209-219.
    • (2004) J. Comput. Appl. Math. , vol.166 , pp. 209-219
    • Liu, F.1    Ann, V.2    Turner, I.3
  • 14
    • 33751548431 scopus 로고    scopus 로고
    • Numerical simulation for solute transport in fractal porous media
    • F. Liu, V. Anh, I. Turner and P. Zhuang, "Numerical simulation for solute transport in fractal porous media", ANZIAM J. 45(E) (2004) 461-173.
    • (2004) ANZIAM J. , vol.45 , Issue.E , pp. 461-1173
    • Liu, F.1    Anh, V.2    Turner, I.3    Zhuang, P.4
  • 16
    • 30244460855 scopus 로고    scopus 로고
    • The fundamental solutions for the fractional diffus ion-wave equation
    • F. Mainardi, "The fundamental solutions for the fractional diffus ion-wave equation", Appl. Math. 9 (1996) 23-28.
    • (1996) Appl. Math. , vol.9 , pp. 23-28
    • Mainardi, F.1
  • 17
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time-fractional diffusion equation
    • F. Mainardi, Yu. Luchko and G. Pagnini, "The fundamental solution of the space-time-fractional diffusion equation", Fract. Calc. Appl. Anal. 4 (2001) 153-192.
    • (2001) Fract. Calc. Appl. Anal. , vol.4 , pp. 153-192
    • Mainardi, F.1    Luchko, Yu.2    Pagnini, G.3
  • 18
    • 28044468843 scopus 로고    scopus 로고
    • Finite difference approximations for two-sided spacefractional partial differential equations
    • M. M. Meerschaert and C. Tadjeran, "Finite difference approximations for two-sided spacefractional partial differential equations", Appl. Numer. Math. 56 (2006) 80-90.
    • (2006) Appl. Numer. Math. , vol.56 , pp. 80-90
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 21
    • 0034275979 scopus 로고    scopus 로고
    • Fractional calculus and continuous-time finance
    • E. Scalas, R. Gorenflo and F. Mainardi, "Fractional calculus and continuous-time finance", Physica A 284 (2000) 376-384.
    • (2000) Physica A , vol.284 , pp. 376-384
    • Scalas, E.1    Gorenflo, R.2    Mainardi, F.3
  • 23
    • 70549107817 scopus 로고    scopus 로고
    • Error analysis of an explicit finite difference approximation for the space-fractional diffusion equation with insulated ends
    • S. Shen and F. Liu, "Error analysis of an explicit finite difference approximation for the space-fractional diffusion equation with insulated ends", ANZIAM J. 46 (2005) 871-887.
    • (2005) ANZIAM J. , vol.46 , pp. 871-887
    • Shen, S.1    Liu, F.2
  • 25
    • 0012721918 scopus 로고    scopus 로고
    • The fractional Black-Scholes equation
    • W. Wyss, "The fractional Black-Scholes equation", Fract. Calc. Appl. Anal. 3 (2000) 51-61.
    • (2000) Fract. Calc. Appl. Anal. , vol.3 , pp. 51-61
    • Wyss, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.