Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 39, Issue 48, Pages 14895-14910Publisher
IOP Publishing Ltd
DOI: 10.1088/0305-4470/39/48/005
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Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class.
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