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Dynamics with low-level fractionality

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

Abstract

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order α<2 is dissipation. In systems with many spacially coupled elements (oscillators) the fractional derivative, along the space coordinate, corresponds to a long range interaction. We discuss a method of constructing a solution using an expansion in ɛ=n-α with small ɛ and positive integer n. The method is applied to the fractional linear and nonlinear oscillators and to fractional Ginzburg–Landau or parabolic equations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:368:y:2006:i:2:p:399-415
    DOI: 10.1016/j.physa.2005.12.015
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    Citations

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    Cited by:

    1. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Taneco-Hernández, M.A., 2018. "Fractional conformable derivatives of Liouville–Caputo type with low-fractionality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 424-438.
    2. Herrmann, Richard, 2010. "Common aspects of q-deformed Lie algebras and fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4613-4622.
    3. 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.
    4. Natalya Ayzenberg & Igor Bykadorov & Sergey Kokovin, 2018. "Optimal Reciprocal Import Tariffs Under Variable Elasticity Of Substitution," HSE Working papers WP BRP 204/EC/2018, National Research University Higher School of Economics.

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