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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 5
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Articles

Well-posedness of fractional Ginzburg–Landau equation in Sobolev spaces

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Pages 1074-1084 | Received 22 Jul 2011, Accepted 12 Dec 2011, Published online: 18 Jan 2012

References

  • Kilbas , A , Srivastava , H and Trujillo , J . 2006 . Theory and Applications of Fractional Differential Equations , Amsterdam : Elsevier .
  • Zaslavsky , G . 2005 . Hamiltonian Chaos and Fractional Dynamics , Oxford : Oxford University Press .
  • Hilfer , R . 2000 . Applications of Fractional Calculus in Physics , Singapore : World Scientific .
  • Carpinteri , A and Mainardi , F . 1997 . Fractals and Fractional Calculus in Continuum Mechanics , New York : Springer .
  • Tarasov , V . 2005 . Continuous medium model for fractal media . Phys. Lett. A. , 336 : 167 – 174 .
  • Wilk , G and Wlodarczyk , Z . 1999 . Do we observe Levy flights in cosmic rays? . Nucl. Phys. , B 75A : 191 – 193 .
  • Naber , M . 2004 . Time fraction Schrödinger equation . J. Math. Phys. , 45 : 3339 – 3352 .
  • Zaslavsky , G and Edelman , A . 2004 . Fractional kinetics: From pseudochaotic dynamics to Maxwell's demon . Physica D. , 193 : 128 – 147 .
  • Mainardi , F and Gorenflo , R . 2000 . On Mittag-Leffler-type functions in fractional evolution processes . J. Comput. Appl. Math. , 118 : 283 – 299 .
  • Weitzner , H and Zaslavdky , G . 2003 . Some applications of fractional derivatives . Commun. Nonlinear Sci. Numer. Simul. , 8 : 273 – 281 .
  • Tarasov , V and Zaslavsky , G . 2006 . Fractional dynamics of coupled oscillators with long-range interaction . Chaos. , 16 : 023110
  • Nec , Y , Nepomnyashchy , A and Golovin , A . 2008 . Oscillatory instability in super-diffusive reaction-diffusion systems: Fractional amplitude and phase diffusion equations . Phys. Rev. E. , 78 : 060102
  • Tarasov , V and Zaslavsky , G . 2005 . Fractional Ginzburg–Landau equation for fractal media . Physica A , 354 : 249 – 261 .
  • Milovanov , A and Rasmussen , J . 2005 . Fractional generalization of the Ginzburg–Landau equation: An unconventional approach to critical phenomena in complex media . Phys. Lett. A. , 337 : 75 – 80 .
  • Tarasov , V . 2006 . Psi-series solution of fractional Ginzburg–Landau equation . J. Phys. A: Math. Gen. , 39 : 8395 – 8407 .
  • Wu , J . 2001 . Dissipative quasi-geostrophic equations with L p data . Electron J. Differ. Eqns , 2001 : 1 – 13 .
  • Pazy , A . 1983 . Semigroups of Linear Operators and Applications to Partial Differetial Equations , New York : Springer-Verlag .
  • Guo , B , Huang , H and Jiang , M . 2002 . Ginzburg–Landau Equation, Chinese ed. , Beijing , , China : Science Press .
  • Crdoba , A and Crdoba , D . 2004 . A maximum principle applied to quasi-geostrophic equations . Commun. Math. Phys. , 249 : 511 – 528 .

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