Relationships between power-law long-range interactions and fractional mechanics

Ryosuke Ishiwata, Yuki Sugiyama

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We investigate the relationships between models of power-law long-range interactions and mechanics based on fractional derivatives. We present the fractional Lagrangian density which gives the Euler-Lagrange equation that serves as the equation of motion for fractional-power-law long-range interactions. We derive this equation by the fractional variational method. In addition, we derive a Noether-like current from the fractional Lagrangian density.

Original languageEnglish
Pages (from-to)5827-5838
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Issue number23
Publication statusPublished - 2012 Dec 1


  • Fractional calculus
  • Fractional variational method
  • Lattice dynamics
  • Long-range interaction


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