Lattice fractional calculus

Vasily E. Tarasov

Applied Mathematics and Computation, 2015, vol. 257, issue C, 12-33

Abstract: Integration and differentiation of non-integer orders for N-dimensional physical lattices with long-range particle interactions are suggested. The proposed lattice fractional derivatives and integrals are represented by kernels of lattice long-range interactions, such that their Fourier series transformations have a power-law form with respect to components of wave vector. Continuous limits for these lattice fractional derivatives and integrals give the continuum derivatives and integrals of non-integer orders with respect to coordinates. Lattice analogs of fractional differential equations that include suggested lattice differential and integral operators can serve as an important element of microscopic approach to nonlocal continuum models in mechanics and physics.

Keywords: Fractional calculus; Lattice models; Fractional derivative; Fractional integral; Nonlocal continuum; Fractional dynamics (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300314015562
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:12-33

DOI: 10.1016/j.amc.2014.11.033

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().