Abstract and Applied Analysis

Nonlocal Boundary Value Problem for Nonlinear Impulsive q k -Integrodifference Equation

Lihong Zhang, Dumitru Baleanu, and Guotao Wang

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


A nonlinear impulsive integrodifference equation within the frame of q k -quantum calculus is investigated by applying using fixed point theorems. The conditions for existence and uniqueness of solutions are obtained.

Article information

Abstr. Appl. Anal., Volume 2014 (2014), Article ID 478185, 6 pages.

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Zhang, Lihong; Baleanu, Dumitru; Wang, Guotao. Nonlocal Boundary Value Problem for Nonlinear Impulsive ${q}_{k}$ -Integrodifference Equation. Abstr. Appl. Anal. 2014 (2014), Article ID 478185, 6 pages. doi:10.1155/2014/478185. https://projecteuclid.org/euclid.aaa/1412273230

Export citation


  • K. S. Miller and B. Ross, “Fractional difference calculus,” in Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications, Series in Mathematics & Its Applications, Horwood, Chichester, 1989, pp.139-152, Nihon University, Koriyama, Japan, May 1988.
  • 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 S. Senguel, “Modeling with fractional difference equations,” Journal of Mathematical Analysis and Applications, vol. 369, no. 1, pp. 1–9, 2010.
  • T. Abdeljawad, D. Baleanu, F. Jarad, and R. P. Agarwal, “Fractional sums and differences with binomial coefficients,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 104173, 6 pages, 2013.
  • G. A. Anastassiou, “Principles of delta fractional calculus on time scales and inequalities,” Mathematical and Computer Modelling, vol. 52, no. 3-4, pp. 556–566, 2010.
  • G. C. Wu and D. Baleanu, “Discrete fractional logistic map and its chaos,” Nonlinear Dynamics, vol. 75, no. 1-2, pp. 283–287, 2014.
  • M. T. Holm, The Theory of Discrete Fractional Calculus: Development and Application [Ph.D. thesis], University of Nebraska-Lincoln, Lincoln, Nebraska, 2011.
  • V. Kac and P. Cheung, Quantum Calculus, Springer, 2002.
  • J. Tariboon and S. K. Ntouyas, “Quantum calculus on finite intervals and applications to impulsive difference equations,” Advances in Difference Equations, vol. 2013, no. 282, 2013.
  • J. X. Sun, Nonlinear Functional Analysis and Its Application, Science Press, Beijing, China, 2008. \endinput