{
  "annotation_id": "ba65a8f0-4f46-4a6a-ab12-5b1a9bd5325a",
  "date_created": "2026-03-02T18:01:04.300000Z",
  "date_modified": "2026-03-02T18:01:04.300000Z",
  "file_hash": "493dea10ad94cb87894ff7e406808550262623aba96ed5e63aef447498c69ac5",
  "private": false,
  "record": {
    "abstract": "The notion of fractional dynamics is related to equations of motion with one\nor a few terms with derivatives of a fractional order. This type of equation\nappears in the description of chaotic dynamics, wave propagation in fractal\nmedia, and field theory. For the fractional linear oscillator the physical\nmeaning of the derivative of order $\\alpha\u003c2$ is dissipation. In systems with\nmany spacially coupled elements (oscillators) the fractional derivative, along\nthe space coordinate, corresponds to a long range interaction. We discuss a\nmethod of constructing a solution using an expansion in $\\epsilon=n-\\alpha$\nwith small $\\epsilon$ and positive integer $n$. The method is applied to the\nfractional linear and nonlinear oscillators and to fractional Ginzburg-Landau\nor parabolic equations.",
    "arxiv_id": "physics/0511138",
    "authors": [
      "Vasily E. Tarasov",
      "George M. Zaslavsky"
    ],
    "categories": [
      "physics.class-ph",
      "cond-mat.other",
      "math-ph",
      "math.DS",
      "math.MP",
      "nlin.CD",
      "physics.gen-ph"
    ],
    "doi": "10.1016/j.physa.2005.12.015",
    "journal_ref": "Physica A. Vol.368. No.2. (2006) 399-415",
    "title": "Dynamics with Low-Level Fractionality",
    "url": "https://arxiv.org/abs/physics/0511138"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fc8567fb-d31d-4056-9ed5-ea1edfa7eb3c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}