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Author Country (or Countries)

Russia

Abstract

A relationship between discrete and continuous fractional-order nonlocal elasticity theory is discussed. As a discrete system we consider three-dimensional lattice with long-range interactions that are described by fractional-order lattice operators.We prove that the continuous limit of suggested three-dimensional lattice equations gives continuum differential equations with the Riesz derivatives of non-integer orders. The proposed lattice models give a new microstructural basis for elasticity of materials with power-law type of non-locality. Moreover these lattice models allow us to have a unified microscopic description for fractional and usual (non-fractional) gradient elasticity continuum.

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