Symmetric duality for left and right Riemann-Liouville and Caputo fractional differences
Classical Analysis and ODEs
2017-06-16 v1
Abstract
A discrete version of the symmetric duality of Caputo-Torres, to relate left and right Riemann-Liouville and Caputo fractional differences, is considered. As a corollary, we provide an evidence to the fact that in case of right fractional differences, one has to mix between nabla and delta operators. As an application, we derive right fractional summation by parts formulas and left fractional difference Euler-Lagrange equations for discrete fractional variational problems whose Lagrangians depend on right fractional differences.
Keywords
Cite
@article{arxiv.1607.03458,
title = {Symmetric duality for left and right Riemann-Liouville and Caputo fractional differences},
author = {Thabet Abdeljawad and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1607.03458},
year = {2017}
}
Comments
This is a preprint of a paper whose final and definite form is published open access in the 'Arab Journal of Mathematical Sciences' (ISSN: 1319-5166), available at [http://dx.doi.org/10.1016/j.ajmsc.2016.07.001]