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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 406910, 12 pages
On Delta and Nabla Caputo Fractional Differences and Dual Identities
1Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
2Department of Mathematics, Çankaya University, 06530 Ankara, Turkey
Received 13 January 2013; Accepted 14 June 2013
Academic Editor: Shurong Sun
Copyright © 2013 Thabet Abdeljawad. 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.
- Dorota Mozyrska, and Ewa Girejko, “On Solutions to Fractional Discrete Systems with Sequential h-Differences,” Abstract and Applied Analysis, 2013.
- Ioannis K. Dassios, and Dumitru I. Baleanu, “Duality of singular linear systems of fractional nabla difference equations,” Applied Mathematical Modelling, 2014.
- Mohamad Rafi Segi Rahmat, “Integral Transform Methods for Solving Fractional Dynamic Equations on Time Scales,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014.
- Weidong Lv, “Solvability for a Discrete Fractional Three-Point Boundary Value Problem at Resonance,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- Guo-Cheng Wu, Dumitru Baleanu, Zhen-Guo Deng, and Sheng-Da Zeng, “Lattice fractional diffusion equation in terms of a Riesz–Caputo difference,” Physica A: Statistical Mechanics and its Applications, 2015.
- Guo-Cheng Wu, Dumitru Baleanu, He-Ping Xie, and Sheng-Da Zeng, “Lattice fractional diffusion equation of random order,” Mathematical Methods in the Applied Sciences, 2015.
- Weidong Lv, “Existence and Uniqueness of Solutions for a Discrete Fractional Mixed Type Sum-Difference Equation Boundary Value Problem,” Discrete Dynamics in Nature and Society, vol. 2015, pp. 1–10, 2015.
- Saowaluk Chasreechai, Chanakarn Kiataramkul, and Thanin Sitthiwirattham, “On Nonlinear Fractional Sum-Difference Equations via Fractional Sum Boundary Conditions Involving Different Orders,” Mathematical Problems in Engineering, vol. 2015, pp. 1–8, 2015.
- 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.
- Lynn Erbe, Christopher S Goodrich, Baoguo Jia, and Allan Peterson, “Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions,” Advances in Difference Equations, vol. 2016, no. 1, 2016.
- M. Ganji, and F. Gharari, “Bayesian Estimation in Delta and Nabla Discrete Fractional Weibull Distributions,” Journal of Probability and Statistics, vol. 2016, pp. 1–8, 2016.