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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 459161, 7 pages
http://dx.doi.org/10.1155/2013/459161
Research Article

Existence and Ulam Stability of Solutions for Discrete Fractional Boundary Value Problem

1Department of Mathematics, Xiangnan University, Chenzhou 423000, China
2School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411005, China

Received 28 May 2013; Accepted 9 July 2013

Academic Editor: Shurong Sun

Copyright © 2013 Fulai Chen and Yong Zhou. 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.

Linked References

  1. G. A. Anastassiou, “Nabla discrete fractional calculus and nabla inequalities,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 562–571, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. T. Abdeljawad, “On Riemann and Caputo fractional differences,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1602–1611, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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. View at MathSciNet
  5. F. M. Atıcı and P. W. Eloe, “Discrete fractional calculus with the nabla operator,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 3, pp. 1–12, 2009. View at Zentralblatt MATH · View at MathSciNet
  6. F. M. Atıcı and S. Şengül, “Modeling with fractional difference equations,” Journal of Mathematical Analysis and Applications, vol. 369, no. 1, pp. 1–9, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. A. C. Ferreira, “A discrete fractional Gronwall inequality,” Proceedings of the American Mathematical Society, vol. 140, no. 5, pp. 1605–1612, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Chen, X. Luo, and Y. Zhou, “Existence results for nonlinear fractional difference equation,” Advances in Difference Equations, vol. 2011, Article ID 713201, 12 pages, 2011. View at Zentralblatt MATH · View at MathSciNet
  9. F. Chen, “Fixed points and asymptotic stability of nonlinear fractional difference equations,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 39, pp. 1–18, 2011. View at MathSciNet
  10. F. Chen and Z. Liu, “Asymptotic stability results for nonlinear fractional difference equations,” Journal of Applied Mathematics, vol. 2012, Article ID 879657, 14 pages, 2012. View at Zentralblatt MATH · View at MathSciNet
  11. C. S. Goodrich, “Existence of a positive solution to a system of discrete fractional boundary value problems,” Applied Mathematics and Computation, vol. 217, no. 9, pp. 4740–4753, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. C. S. Goodrich, “On discrete sequential fractional boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 385, no. 1, pp. 111–124, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. W. Lv, “Existence of solutions for discrete fractional boundary value problems with a p-Laplacian operator,” Advances in Difference Equations, vol. 2012, article 163, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Wang, L. Lv, and Y. Zhou, “Ulam stability and data dependence for fractional differential equations with Caputo derivative,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 63, pp. 1–10, 2011. View at MathSciNet
  15. A. N. Kolmogorov and S. V. Fomin, Elements of Function Theory and Functional Analysis, Nauka, Moscow, Russia, 1981.
  16. R. P. Agarwal, M. Meehan, and D. O'Regan, Fixed Point Theory and Applications, vol. 141 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, UK, 2001. View at Publisher · View at Google Scholar · View at MathSciNet