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Title: Symmetric duality for left and right Riemann-Liouville and Caputo fractional differences
Author: Abdeljawad, Thabet
Torres, Delfim F. M.
Keywords: Right (left) delta and nabla fractional sums
Right (left) delta and nabla fractional differences
Symmetric duality
The Q-operator
Summation by parts
Discrete fractional calculus
Issue Date: 2017
Publisher: Elsevier
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.
Peer review: yes
DOI: 10.1016/j.ajmsc.2016.07.001
ISSN: 1319-5166
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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