Fractional-order difference equations for physical lattices and some applications

Journal Article · Thu Oct 15 04:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4933028· OSTI ID:22479549

Fractional-order operators for physical lattice models based on the Grünwald-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 Grünwald-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.

• OSTI ID: 22479549
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 56; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COORDINATES
INTEGRALS
INTERACTION RANGE
KERNELS
MAXWELL EQUATIONS
NAVIER-STOKES EQUATIONS
PARTICLE INTERACTIONS