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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 410505, 8 pages
A Study of Nonlinear Fractional -Difference Equations with Nonlocal Integral Boundary Conditions
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Received 12 July 2013; Revised 9 September 2013; Accepted 9 September 2013
Academic Editor: Dumitru Baleanu
Copyright © 2013 Ahmed Alsaedi 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.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Eds., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach Science, Yverdon, Switzerland, 1993.
- D. Băleanu and O. G. Mustafa, “On the global existence of solutions to a class of fractional differential equations,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1835–1841, 2010.
- D. Băleanu, O. G. Mustafa, and R. P. Agarwal, “On -solutions for a class of sequential fractional differential equations,” Applied Mathematics and Computation, vol. 218, no. 5, pp. 2074–2081, 2011.
- R. P. Agarwal and B. Ahmad, “Existence theory for anti-periodic boundary value problems of fractional differential equations and inclusions,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1200–1214, 2011.
- B. Ahmad and J. J. Nieto, “Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions,” Boundary Value Problems, vol. 2011, article 36, 2011.
- S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, and R. Magin, “Fractional Bloch equation with delay,” Computers & Mathematics with Applications, vol. 61, no. 5, pp. 1355–1365, 2011.
- F. T. Akyildiz, H. Bellout, K. Vajravelu, and R. A. Van Gorder, “Existence results for third order nonlinear boundary value problems arising in nano boundary layer fluid flows over stretching surfaces,” Nonlinear Analysis. Real World Applications, vol. 12, no. 6, pp. 2919–2930, 2011.
- B. Ahmad and J. J. Nieto, “Sequential fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 64, no. 10, pp. 3046–3052, 2012.
- J. R. Graef, L. Kong, and Q. Kong, “Application of the mixed monotone operator method to fractional boundary value problems,” Fractional Differential Calculus, vol. 2, pp. 554–567, 2011.
- R. P. Agarwal, “Certain fractional -integrals and -derivatives,” Proceedings of the Cambridge Philosophical Society, vol. 66, pp. 365–370, 1969.
- W. A. Al-Salam, “Some fractional -integrals and -derivatives,” Proceedings of the Edinburgh Mathematical Society, vol. 15, pp. 135–140, 1966.
- F. M. Atici and P. W. Eloe, “Fractional -calculus on a time scale,” Journal of Nonlinear Mathematical Physics, vol. 14, no. 3, pp. 333–344, 2007.
- F. M. Atici and P. W. Eloe, “Linear systems of fractional nabla difference equations,” The Rocky Mountain Journal of Mathematics, vol. 41, no. 2, pp. 353–370, 2011.
- F. M. Atıcı and P. W. Eloe, “Two-point boundary value problems for finite fractional difference equations,” Journal of Difference Equations and Applications, vol. 17, no. 4, pp. 445–456, 2011.
- M. El-Shahed and F. M. Al-Askar, “Positive solutions for boundary value problem of nonlinear fractional -difference equation,” ISRN Mathematical Analysis, vol. 2011, Article ID 385459, 12 pages, 2011.
- R. A. C. Ferreira, “Positive solutions for a class of boundary value problems with fractional -differences,” Computers & Mathematics with Applications, vol. 61, no. 2, pp. 367–373, 2011.
- R. A. C. Ferreira, “Nontrivial solutions for fractional -difference boundary value problems,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 70, pp. 1–10, 2010.
- C. S. Goodrich, “Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions,” Computers & Mathematics with Applications, vol. 61, no. 2, pp. 191–202, 2011.
- J. R. Graef and L. Kong, “Positive solutions for a class of higher order boundary value problems with fractional -derivatives,” Applied Mathematics and Computation, vol. 218, no. 19, pp. 9682–9689, 2012.
- J. Ma and J. Yang, “Existence of solutions for multi-point boundary value problem of fractional -difference equation,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 92, pp. 1–10, 2011.
- G. C. Wu and D. Baleanu, “New applications of the variational iteration methodfrom differential equations to q-fractional difference equations,” Advances in Difference Equations, vol. 2013, article 21, 2013.
- F. Jarad, T. Abdeljawad, and D. Baleanu, “Stability of -fractional non-autonomous systems,” Nonlinear Analysis. Real World Applications, vol. 14, no. 1, pp. 780–784, 2013.
- B. Ahmad, S. K. Ntouyas, and I. K. Purnaras, “Existence results for nonlocal boundary value problems of nonlinear fractional q-difference equations,” Advances in Difference Equations, vol. 2012, article 140, 2012.
- P. M. Rajković, S. D. Marinković, and M. S. Stanković, “Fractional integrals and derivatives in -calculus,” Applicable Analysis and Discrete Mathematics, vol. 1, no. 1, pp. 311–323, 2007.
- M. H. Annaby and Z. S. Mansour, q-Fractional Calculus and Equations, vol. 2056 of Lecture Notes in Mathematics, Springer, Heidelberg, Germany, 2012.
- P. M. Rajković, S. D. Marinković, and M. S. Stanković, “On -analogues of Caputo derivative and Mittag-Leffler function,” Fractional Calculus & Applied Analysis, vol. 10, no. 4, pp. 359–373, 2007.
- A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer, New York, NY, USA, 2005.
- D. R. Smart, Fixed Point Theorems, Cambridge University Press, 1980.