Journal
CENTRAL EUROPEAN JOURNAL OF PHYSICS
Volume 11, Issue 11, Pages 1580-1588Publisher
VERSITA
DOI: 10.2478/s11534-013-0308-z
Keywords
fractional derivatives; lattice model; spatial dispersion; elasticity; fractional elasticity
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A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations for the lattice with the power-law spatial dispersion into the continuum equations with fractional generalizations of the Laplacian operators. The suggested continuum equations, which are obtained from the lattice model, are fractional generalizations of the integral and gradient elasticity models. These equations of fractional elasticity are solved for two special static cases: fractional integral elasticity and fractional gradient elasticity.
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