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.
|Number of pages||12|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 2012 Dec 1|
- Fractional calculus
- Fractional variational method
- Lattice dynamics
- Long-range interaction