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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.
- R. P. Agarwal, “Certain fractional q-integrals and q-derivatives,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 66, pp. 365–370, 1969.
- J. B. Diaz and T. J. Osler, “Differences of fractional order,” Mathematics of Computation, vol. 28, pp. 185–202, 1974.
- H. L. Gray and N. F. Zhang, “On a new definition of the fractional difference,” Mathematics of Computation, vol. 50, no. 182, pp. 513–529, 1988.
- K. S. Miller and B. Ross, “Fractional difference calculus,” in Univalent Functions, Fractional Calculus, and Their Applications (Koriyama, 1988), Ellis Horwood Series: Mathematics and Its Applications, pp. 139–152, Horwood, Chichester, UK, 1989.
- F. M. Atici and P. W. Eloe, “A transform method in discrete fractional calculus,” International Journal of Difference Equations, vol. 2, no. 2, pp. 165–176, 2007.
- F. M. Atici and P. W. Eloe, “Fractional q-calculus on a time scale,” Journal of Nonlinear Mathematical Physics, vol. 14, no. 3, pp. 341–352, 2007.
- J. Čermák and L. Nechvátal, “On (q, h)-analogue of fractional calculus,” Journal of Nonlinear Mathematical Physics, vol. 17, no. 1, pp. 51–68, 2010.
- M. Bohner and A. Peterson, Dynamic equations on time scales, Birkhauser, Boston, Mass, USA, 2001.
- M. Bohner and A. Peterso, Eds., Advances in Dynamic Equations on Time Scales, Birkhauser, Boston, Mass, USA, 2003.
- G. A. Anastassiou, “Foundations of nabla fractional calculus on time scales and inequalities,” Computers & Mathematics with Applications, vol. 59, no. 12, pp. 3750–3762, 2010.
- G. E. Andrews, R. Askey, and R. Roy, Special Functions, vol. 71 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 1999.
- F. M. Atici and P. W. Eloe, “Initial value problems in discrete fractional calculus,” Proceedings of the American Mathematical Society, vol. 137, no. 3, pp. 981–989, 2009.
- F. M. Atici and P. W. Eloe, “Discrete fractional calculus with the nabla operator,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2009, no. 2, p. 12, 2009.
- Z. S. I. Mansour, “Linear sequential q-difference equations of fractional order,” Fractional Calculus & Applied Analysis, vol. 12, no. 2, pp. 159–178, 2009.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- A. Nagai, “On a certain fractional q-difference and its eigen function,” Journal of Nonlinear Mathematical Physics, vol. 10, supplement 2, pp. 133–142, 2003.
- J. Čermák and T. Kisela, “Note on a discretization of a linear fractional differential equation,” Mathematica Bohemica, vol. 135, no. 2, pp. 179–188, 2010.
- A. A. Kilbas, M. Saigo, and R. K. Saxena, “Solution of Volterra integrodifferential equations with generalized Mittag-Leffler function in the kernels,” Journal of Integral Equations and Applications, vol. 14, no. 4, pp. 377–396, 2002.
- A. A. Kilbas, M. Saigo, and R. K. Saxena, “Generalized Mittag-Leffler function and generalized fractional calculus operators,” Integral Transforms and Special Functions, vol. 15, no. 1, pp. 31–49, 2004.
- F. M. Atici and P. W. Eloe, “Linear systems of fractional nabla difference equations,” Rocky Mountain Journal of Mathematics, vol. 41, pp. 353–370, 2011.