Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 47, Issue 9, Pages -Publisher
AIP Publishing
DOI: 10.1063/1.2337852
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Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the continuous limit is discussed. The one-dimensional systems of coupled oscillators for this type of long-range interactions are considered. The discrete equations of motion are mapped into the continuum equation with the Riesz fractional derivative. (c) 2006 American Institute of Physics.
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