Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 56, Issue 10, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4933028
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Fractional-order operators for physical lattice models based on the Grunwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grunwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions. Continuum limits of these fractional-order difference equations are also suggested. (C) 2015 AIP Publishing LLC.
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