Lattice with long-range interaction of power-law type for fractional non-local elasticity |
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Institution: | Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia |
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Abstract: | Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with Riesz derivatives of non-integer orders. The continuum equations that are obtained from the lattice model describe fractional generalization of non-local elasticity models. Particular solutions and correspondent asymptotic of the fractional differential equations for displacement fields are suggested for the static case. |
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Keywords: | Fractional elasticity Lattice model Long-range interaction Fractional dynamics Non-local elasticity |
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