메뉴 건너뛰기




Volumn 59, Issue 5, 2010, Pages 1754-1758

Anomalous diffusion modeling by fractal and fractional derivatives

Author keywords

Anomalous diffusion; Fractal derivative; Fractional derivative; Heavy tail; Power law

Indexed keywords

ANOMALOUS DIFFUSION; DERIVATIVE MODELS; DIFFUSION VELOCITY; FRACTIONAL DERIVATIVE MODEL; FRACTIONAL DERIVATIVES; FUNDAMENTAL SOLUTIONS; HEAVY-TAILS; NEW MODEL; POWER LAW;

EID: 76449111034     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.08.020     Document Type: Article
Times cited : (454)

References (24)
  • 1
    • 33745725683 scopus 로고    scopus 로고
    • A speculative study of 2/3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures
    • Chen W. A speculative study of 2/3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures. Chaos 16 (2006) 023126
    • (2006) Chaos , vol.16 , pp. 023126
    • Chen, W.1
  • 2
  • 4
    • 33750456214 scopus 로고    scopus 로고
    • Numerical investigations of anomalous diffusion effects in glasses
    • Schulz B.M., and Schulz M. Numerical investigations of anomalous diffusion effects in glasses. Journal of Non-Crystalline Solids 352 (2006) 4884-4887
    • (2006) Journal of Non-Crystalline Solids , vol.352 , pp. 4884-4887
    • Schulz, B.M.1    Schulz, M.2
  • 6
    • 0034832088 scopus 로고    scopus 로고
    • The fractional Fick's law for non-local transport processes
    • Paradisia P., Cesari R., Mainardi F., and Tampieri F. The fractional Fick's law for non-local transport processes. Physica A 293 (2001) 130-142
    • (2001) Physica A , vol.293 , pp. 130-142
    • Paradisia, P.1    Cesari, R.2    Mainardi, F.3    Tampieri, F.4
  • 7
    • 34249805393 scopus 로고    scopus 로고
    • Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation
    • Zhang H., Liu F., and Anh V. Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation. Journal of Computational and Applied Mathematics 206 (2007) 1098-1115
    • (2007) Journal of Computational and Applied Mathematics , vol.206 , pp. 1098-1115
    • Zhang, H.1    Liu, F.2    Anh, V.3
  • 8
    • 27744450698 scopus 로고    scopus 로고
    • Time-space fabric underlying anomalous diffusion
    • Chen W. Time-space fabric underlying anomalous diffusion. Chaos, Solitons and Fractals 28 (2006) 923-929
    • (2006) Chaos, Solitons and Fractals , vol.28 , pp. 923-929
    • Chen, W.1
  • 10
    • 0032491749 scopus 로고    scopus 로고
    • Representation of random walk in fractal space-time
    • Kanno R. Representation of random walk in fractal space-time. Physica A 248 (1998) 165-175
    • (1998) Physica A , vol.248 , pp. 165-175
    • Kanno, R.1
  • 12
    • 0000361678 scopus 로고    scopus 로고
    • Random walk models for space-fractional diffusion processes
    • Gorenflo R., and Mainardi F. Random walk models for space-fractional diffusion processes. Fractional Calculus Applied Analysis 1 (1998) 167-191
    • (1998) Fractional Calculus Applied Analysis , vol.1 , pp. 167-191
    • Gorenflo, R.1    Mainardi, F.2
  • 13
    • 1642641759 scopus 로고    scopus 로고
    • Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency
    • Chen W., and Holm S. Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency. Journal of the Acoustical Society of America 115 4 (2004) 1424-1430
    • (2004) Journal of the Acoustical Society of America , vol.115 , Issue.4 , pp. 1424-1430
    • Chen, W.1    Holm, S.2
  • 14
    • 0030526052 scopus 로고    scopus 로고
    • Universality Classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential
    • Vlad M.O., Metzler R., Nonnenmacher T.F., and Mackey M.C. Universality Classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential. J. Math. Phys. 37 (1996) 2279-2306
    • (1996) J. Math. Phys. , vol.37 , pp. 2279-2306
    • Vlad, M.O.1    Metzler, R.2    Nonnenmacher, T.F.3    Mackey, M.C.4
  • 15
    • 34047203146 scopus 로고    scopus 로고
    • V-Langevin equations, continuous time random walks and fractional diffusion
    • Balescu R. V-Langevin equations, continuous time random walks and fractional diffusion. Chaos, Solitons and Fractals 34 (2007) 62-80
    • (2007) Chaos, Solitons and Fractals , vol.34 , pp. 62-80
    • Balescu, R.1
  • 16
    • 0001407424 scopus 로고    scopus 로고
    • The fundamental solution of the space-time fractional diffusion equation
    • Mainardi F., Luchko Y., and Pagnini G. The fundamental solution of the space-time fractional diffusion equation. Fractional Calculus and Applied Analysis 4 2 (2001) 153-192
    • (2001) Fractional Calculus and Applied Analysis , vol.4 , Issue.2 , pp. 153-192
    • Mainardi, F.1    Luchko, Y.2    Pagnini, G.3
  • 17
    • 34547102267 scopus 로고    scopus 로고
    • The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
    • Mainardi F., and Pagnini G. The role of the Fox-Wright functions in fractional sub-diffusion of distributed order. Journal of Computational and Applied Mathematics 207 (2007) 245-257
    • (2007) Journal of Computational and Applied Mathematics , vol.207 , pp. 245-257
    • Mainardi, F.1    Pagnini, G.2
  • 18
    • 28044468843 scopus 로고    scopus 로고
    • Finite difference approximations for two-sided space-fractional partial differential equations
    • Meerschaert M.M., and Tadjeran C. Finite difference approximations for two-sided space-fractional partial differential equations. Applied Numerical Mathematics 56 (2006) 80-90
    • (2006) Applied Numerical Mathematics , vol.56 , pp. 80-90
    • Meerschaert, M.M.1    Tadjeran, C.2
  • 19
    • 53449087859 scopus 로고    scopus 로고
    • Simulation of the continuous time random walk of the space-fractional diffusion equations
    • Abdel-Rehim E.A., and Gorenflo R. Simulation of the continuous time random walk of the space-fractional diffusion equations. Journal of Computational and Applied Mathematics 222 2 (2008) 274-283
    • (2008) Journal of Computational and Applied Mathematics , vol.222 , Issue.2 , pp. 274-283
    • Abdel-Rehim, E.A.1    Gorenflo, R.2
  • 20
    • 15544368331 scopus 로고    scopus 로고
    • Discrete and continuous random walk models for space-time fractional diffusion
    • Gorenflo R., Vivoli A., and Mainardi F. Discrete and continuous random walk models for space-time fractional diffusion. Nonlinear dynamics 38 (2004) 101-116
    • (2004) Nonlinear dynamics , vol.38 , pp. 101-116
    • Gorenflo, R.1    Vivoli, A.2    Mainardi, F.3
  • 21
    • 31644435275 scopus 로고    scopus 로고
    • Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion
    • Abe S., and Thurner S. Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion. Physica A 356 (2005) 403-407
    • (2005) Physica A , vol.356 , pp. 403-407
    • Abe, S.1    Thurner, S.2
  • 22
    • 33751161217 scopus 로고    scopus 로고
    • A review of anomalous diffusion phenomena at fractal interface for diffusion-controlled and non-diffusion-controlled transfer processes
    • Go J.-Y., and Pyun S.-I. A review of anomalous diffusion phenomena at fractal interface for diffusion-controlled and non-diffusion-controlled transfer processes. Journal of Solid State Electrochemistry 11 (2007) 323-334
    • (2007) Journal of Solid State Electrochemistry , vol.11 , pp. 323-334
    • Go, J.-Y.1    Pyun, S.-I.2
  • 23
    • 34547673244 scopus 로고    scopus 로고
    • Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
    • Liu F., Zhuang P., Anh V., Turner I., and Burrage K. Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation. Applied Mathematics and Computation 191 (2007) 12-20
    • (2007) Applied Mathematics and Computation , vol.191 , pp. 12-20
    • Liu, F.1    Zhuang, P.2    Anh, V.3    Turner, I.4    Burrage, K.5
  • 24
    • 34547548712 scopus 로고    scopus 로고
    • Finite difference/spectral approximations for the time-fractional diffusion equation
    • Lin Y., and Xu C. Finite difference/spectral approximations for the time-fractional diffusion equation. Journal of Computational Physics 225 (2007) 1533-1552
    • (2007) Journal of Computational Physics , vol.225 , pp. 1533-1552
    • Lin, Y.1    Xu, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.