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Fractional Ginzburg–Landau equation for fractal media

Author

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  • Tarasov, Vasily E.
  • Zaslavsky, George M.

Abstract

We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equation or nonlinear Schrödinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied.

Suggested Citation

  • Tarasov, Vasily E. & Zaslavsky, George M., 2005. "Fractional Ginzburg–Landau equation for fractal media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 249-261.
    • Handle: RePEc:eee:phsmap:v:354:y:2005:i:c:p:249-261
    DOI: 10.1016/j.physa.2005.02.047
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    Citations

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    Cited by:

    1. Heydari, M.H. & Razzaghi, M., 2023. "Piecewise fractional Chebyshev cardinal functions: Application for time fractional Ginzburg–Landau equation with a non-smooth solution," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    2. Korabel, Nickolay & Zaslavsky, George M., 2007. "Transition to chaos in discrete nonlinear Schrödinger equation with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 223-237.
    3. Ivars, Salim B. & Botey, Muriel & Herrero, Ramon & Staliunas, Kestutis, 2023. "Stabilisation of spatially periodic states by non-Hermitian potentials," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. El-Ajou, Ahmad & Abu Arqub, Omar & Al-Smadi, Mohammed, 2015. "A general form of the generalized Taylor’s formula with some applications," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 851-859.
    5. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Zhang, Li & He, Yingji, 2020. "Soliton dynamics in a fractional complex Ginzburg-Landau model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Tarasov, Vasily E. & Zaslavsky, George M., 2007. "Fractional dynamics of systems with long-range space interaction and temporal memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 291-308.
    7. Hong Lu & Linlin Wang & Mingji Zhang, 2022. "Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise," Mathematics, MDPI, vol. 10(23), pages 1-36, November.
    8. Pavlos, G.P. & Karakatsanis, L.P. & Iliopoulos, A.C. & Pavlos, E.G. & Xenakis, M.N. & Clark, Peter & Duke, Jamie & Monos, D.S., 2015. "Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 188-209.
    9. Mahmoud A. Zaky & Ahmed S. Hendy & Rob H. De Staelen, 2021. "Alikhanov Legendre—Galerkin Spectral Method for the Coupled Nonlinear Time-Space Fractional Ginzburg–Landau Complex System," Mathematics, MDPI, vol. 9(2), pages 1-22, January.

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