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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 565067, 21 pages
Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations
Institute of Mathematics, Faculty of Mechanical Engineering, Technická 2, 616 69 Brno, Czech Republic
Received 7 January 2011; Accepted 23 April 2011
Academic Editor: Yuri V. Rogovchenko
Copyright © 2011 Jan Čermák et al. 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.
- Jan Čermák, Tomáš Kisela, and Luděk Nechvátal, “Stability and asymptotic properties of a linear fractional difference equation,” Advances in Difference Equations, vol. 2012, 2012.
- Tomas Kisela, “Power functions and essentials of fractional calculus on isolated time scales,” Advances in Difference Equations, 2013.
- Jan Čermák, Tomáš Kisela, and Luděk Nechvátal, “Stability regions for linear fractional differential systems and their discretizations,” Applied Mathematics and Computation, vol. 219, no. 12, pp. 7012–7022, 2013.
- Ferhan M. Atici, “Exponential Functions Of Discrete Fractional Calculus,” Applicable Analysis And Discrete Mathematics, vol. 7, no. 2, pp. 343–353, 2013.
- Jan Čermák, and Tomáš Kisela, “Exact and discretized stability of the Bagley–Torvik equation,” Journal of Computational and Applied Mathematics, 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.
- Mohamad Rafi Segi Rahmat, and Mohd Salmi Md Noorani, “Caputo type fractional difference operator and its application on discrete time scales,” Advances in Difference Equations, vol. 2015, no. 1, 2015.
- Ferhan M. Atici, and Meltem Uyanik, “Analysis Of Discrete Fractional Operators,” Applicable Analysis And Discrete Mathematics, vol. 9, no. 1, pp. 139–149, 2015.
- I. Area, J. D. Djida, J. Losada, and Juan J. Nieto, “On Fractional Orthonormal Polynomials of a Discrete Variable,” Discrete Dynamics in Nature and Society, vol. 2015, pp. 1–7, 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.
- Feifei Du, Baoguo Jia, Lynn Erbe, and Allan Peterson, “ Monotonicity and convexity for nabla fractional ( q , h )-differences ,” Journal of Difference Equations and Applications, pp. 1–20, 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.