On discrete generalized nabla fractional sums and differences
Abstract
This article investigates a class of discrete nabla fractional operators by using the discrete nabla convolution theorem. Inspired by this, we define the discrete generalized nabla fractional sum and differences of Riemann-Liouville and Caputo types. In the process, we give a relationship between the generalized discrete delta fractional operators introduced by Ferreira \cite{Ferreira} and the proposed discrete generalized nabla fractional operators via the dual identities. Also, we present some test examples to justify the relationship. Moreover, we prove the fundamental theorem of calculus for the defined discrete generalized nabla fractional operators. Inspired by the above operators, we define discrete generalized nabla Atangana-Baleanu-like (or Caputo-Fabrizio-like) fractional sum and differences at the end of the article.
Cite
@article{arxiv.2201.03073,
title = {On discrete generalized nabla fractional sums and differences},
author = {Pshtiwan Othman Mohammed and Thabet Abdeljawad and Faraidun Kadir Hamasalh},
journal= {arXiv preprint arXiv:2201.03073},
year = {2022}
}
Comments
There are some mistakes. I would be very grateful if you could please withdraw it for us as soon as possible