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

Ryosuke Ishiwata; Yuki Sugiyama

doi:10.1016/j.physa.2012.06.055

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

Ryosuke Ishiwata, Yuki Sugiyama

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	5827-5838
Number of pages	12
Journal	Physica A: Statistical Mechanics and its Applications
Volume	391
Issue number	23
DOIs	https://doi.org/10.1016/j.physa.2012.06.055
Publication status	Published - 2012 Dec 1
Externally published	Yes

Keywords

Fractional calculus
Fractional variational method
Lattice dynamics
Long-range interaction

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

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10.1016/j.physa.2012.06.055

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title = "Relationships between power-law long-range interactions and fractional mechanics",

abstract = "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.",

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AU - Ishiwata, Ryosuke

AU - Sugiyama, Yuki

PY - 2012/12/1

Y1 - 2012/12/1

N2 - 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.

AB - 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.

KW - Fractional calculus

KW - Fractional variational method

KW - Lattice dynamics

KW - Long-range interaction

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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