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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 406757, 13 pages
On the Definitions of Nabla Fractional Operators
1Department of Mathematics, Çankaya University, 06530 Ankara, Turkey
2Department of Mathematics, Western Kentucky University, Bowling Green, KY 42101, USA
Received 12 April 2012; Accepted 4 September 2012
Academic Editor: Dumitru Bǎleanu
Copyright © 2012 Thabet Abdeljawad and Ferhan M. Atici. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [12 citations]
The following is the list of published articles that have cited the current article.
- Thabet Abdeljawad, Dumitru Baleanu, Fahd Jarad, and Ravi P. Agarwal, “Fractional Sums and Differences with Binomial Coefficients,” Discrete Dynamics in Nature and Society, vol. 2013, pp. 1–6, 2013.
- Thabet Abdeljawad, “On Delta and Nabla Caputo Fractional Differences and Dual Identities,” Discrete Dynamics in Nature and Society, vol. 2013, pp. 1–12, 2013.
- Ferhan M. Atici, “Exponential Functions Of Discrete Fractional Calculus,” Applicable Analysis And Discrete Mathematics, vol. 7, no. 2, pp. 343–353, 2013.
- J. Jagan Mohan, and G. V. S. R. Deekshitulu, “Solutions of Nabla Fractional Difference Equations Using N-Transforms,” Communications in Mathematics and Statistics, 2014.
- A. Feza Guvenilir, Allan C. Peterson, and Kenan Tas, “Nabla discrete fractional Gruss type inequality,” Journal of Inequalities and Applications, 2014.
- Ioannis K. Dassios, and Dumitru I. Baleanu, “Duality of singular linear systems of fractional nabla difference equations,” Applied Mathematical Modelling, 2014.
- T. Abdeljawad, “On conformable fractional calculus,” Journal of Computational and Applied Mathematics, 2014.
- Carlos Lizama, “lp-maximal regularity for fractional difference equations on UMD spaces,” Mathematische Nachrichten, 2015.
- Thabet Abdeljawad, and Dumitru Baleanu, “Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels,” Advances in Difference Equations, vol. 2016, no. 1, 2016.
- Guo-Cheng Wu, Dumitru Baleanu, and He-Ping Xie, “Riesz Riemann–Liouville difference on discrete domains,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 26, no. 8, pp. 084308, 2016.
- Thabet Abdeljawad, and Delfim F.M. Torres, “Symmetric duality for left and right Riemann–Liouville and Caputo fractional differences,” Arab Journal of Mathematical Sciences, 2016.
- Wei Nian Li, and Weihong Sheng, “Sufficient conditions for oscillation of a nonlinear fractional nabla difference system,” SpringerPlus, vol. 5, no. 1, 2016.