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Original Articles

Some properties of fractional burgers equation

Pages 151-158 | Received 04 Oct 2001, Published online: 14 Oct 2010

References

  • Abraham‐Shrauner , B. and Guo , A. 1993 . “ Hidden and nonlocal symmeries of nonlinear differential equations ” . In Modern Goup Analysis: Advanced Analytical and Computational Methods in Mathematical Physics , 1 – 5 . Dordrecht : Kluver Acad Pb .
  • Agarwal , R.P. and O'Regan , D. 2001 . Integral and Integrodifferential Equations Theory, Methods and Applications , Amsterdam : G & B Science Pub. .
  • Bertotti , G. 1998 . Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers (Electromagnetism. , New York : Academic Press .
  • Clarcson , P.A. and Mansfield , E.L. 1993 . “ Symmetries of nonlinear heat equation, in modern goup analysis ” . In Advanced Analytical and Computational Methods in Mathematical Physics 155 – 171 .
  • Fisher , D.S. and Huse , D.A. 1991 . Directed pathsin a random potential . Phys. Rev. B , 43 : 10728 – 10742 .
  • Gerasimov , A.N. 1948 . A generalization of linear laws of deformation and its application to inner friction problems . Prikl. Mat. Mekh. , 12 : 251 – 259 . (in Russian)
  • Gurbatov , S.N. , Malakhov , A.N. and Saichev , A.I. 1991 . Nonlinem Random Waves and Turbulence in Non‐dissipative Media: Waves, Rays, Particles , Mancester Univ. Press .
  • Hernandez , R.H. , Lavi , D. and Winternitz , P. 1999 . Symmetry preserving discretization of the Burgers Equation
  • Hwa , T. 1992 . Nonequilibrium dynamics of driven line liquids . Phys. Rev. Lett. , 69 : 1552 – 1555 .
  • Hwa , T. and Kardar , M. 1992 . Avalanches, hydrodynamics, and discharge events in models of sandpiles . Phys. Rev. A , 45 : 7002 – 7023 .
  • Kardar , M. , Parisi , G. and Zhang , Z. 1986 . Dynamic scaling of growing interfaces . Phys. Rev. Lett. , : 889 – 892 .
  • Lakes , R. 1998 . Viscoelastic Solids , CRC Mechanical Engineering Series New York : CRC Press .
  • Miškinis , P. 2000 . The nonlinear heterogeneous diffusion equation and distribution of matter in the early universe . The Astrophysical Journal , 543 : L95 – L98 .
  • Nigmatullin , R.R. 1984 . To the theoretical explanation of the ‘universal response’ . Phys. Stat. Sol.(b , 123 : 739 – 745 .
  • Oldham , K.B. and Spanier , J. 1974 . The fractional calculus , New York and London : Acad. Press .
  • Podlubny , I. 1999 . Fractional differential Equations, Ser. Math. Science and Engineering , San Diego : Acad. Press .
  • Samko , S.G. , Kilbas , A.A. and Marichev , O.I. 1987 . Integrals and derivatives of the fractional order and some their applications , Moscow : Nauka .
  • Shandarin , S.F. and Zeldovich , Ya.B. 1989 . Turbulence, intermittency, structures in a self‐graviting medium: the large scale structure of the universe . Rev. Mod. Phys. , 61 : 185 – 220 .
  • Volterra , V. 1931 . Leçons sur la Théorie Mathématique de la Lutte pour la Vie , Paris : Gauthier‐Villars . (Russian translation: Moscow, Nauka, 1976
  • Woyczynski , W.A. 1998 . Burgers‐KPZ Turbulence , New York : Springer .
  • Zeldovich , Ya.B. 1970 . Gravitational instability: An approximate theory for large density perturbations . Astron. and Astroph. , 5 : 84 – 95 .

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