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Fractional dynamics of systems with long-range space interaction and temporal memory

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

Abstract

Field equations with time and coordinate derivatives of noninteger order are derived from a stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a fractional generalization of the Ginzburg–Landau and nonlinear Schrödinger equations. As another example, dynamical equations for particle chains with power-law interaction and memory are considered in the continuous limit. The obtained fractional equations can be applied to complex media with/without random parameters or processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:2:p:291-308
    DOI: 10.1016/j.physa.2007.04.050
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    References listed on IDEAS

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    1. 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.
    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. Zaslavsky, G.M. & Guzdar, P.N. & Edelman, M. & Sitnov, M.I. & Sharma, A.S., 2007. "Selfsimilarity and fractional kinetics of solar wind–magnetosphere coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 11-20.
    4. Laskin, N. & Zaslavsky, G., 2006. "Nonlinear fractional dynamics on a lattice with long range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 38-54.
    5. Tarasov, Vasily E. & Zaslavsky, George M., 2006. "Dynamics with low-level fractionality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(2), pages 399-415.
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    Cited by:

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    2. Maurya, Rahul Kumar & Li, Dongxia & Singh, Anant Pratap & Singh, Vineet Kumar, 2024. "Numerical algorithm for a general fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 405-432.

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