Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 973783, 7 pages
http://dx.doi.org/10.1155/2015/973783
Research Article

On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Received 4 November 2014; Accepted 3 April 2015

Academic Editor: Baodong Zheng

Copyright © 2015 Bashir Ahmad 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.

Linked References

  1. B. Ahmad and J. J. Nieto, “Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory,” Topological Methods in Nonlinear Analysis, vol. 35, no. 2, pp. 295–304, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. Sakthivel, N. I. Mahmudov, and J. J. Nieto, “Controllability for a class of fractional-order neutral evolution control systems,” Applied Mathematics and Computation, vol. 218, no. 20, pp. 10334–10340, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. P. Agarwal, D. O'Regan, and S. Stanek, “Positive solutions for mixed problems of singular fractional differential equations,” Mathematische Nachrichten, vol. 285, no. 1, pp. 27–41, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. C. Zhai and M. Hao, “Mixed monotone operator methods for the existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems,” Boundary Value Problems, vol. 2013, article 85, 13 pages, 2013. View at Publisher · View at Google Scholar
  6. J. R. Wang, Y. Zhou, and M. Feckan, “On the nonlocal Cauchy problem for semilinear fractional order evolution equations,” Central European Journal of Mathematics, vol. 12, no. 6, pp. 911–922, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. R. Graef, L. Kong, and M. Wang, “Existence and uniqueness of solutions for a fractional boundary value problem on a graph,” Fractional Calculus and Applied Analysis, vol. 17, no. 2, pp. 499–510, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. B. Ahmad and J. J. Nieto, “A class of differential equations of fractional order with multi-point boundary conditions,” Georgian Mathematical Journal, vol. 21, no. 3, pp. 243–248, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Henderson and R. Luca, “Positive solutions for a system of nonlocal fractional boundary value problems,” Fractional Calculus and Applied Analysis, vol. 16, no. 4, pp. 985–1008, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. 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, Amsterdam, The Netherlands, 2006. View at MathSciNet
  11. 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.
  12. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, Imperial College Press, London, UK, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  13. J. Klafter, S. C. Lim, and R. Metzler, Eds., Fractional Dynamics in Physics, World Scientific, Singapore, 2011.
  14. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston, Mass, USA, 2012.
  15. J. Wang, Y. Zhou, and W. Wei, “Fractional sewage treatment models with impulses at variable times,” Applicable Analysis, vol. 92, no. 9, pp. 1959–1979, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. X. Liu, Z. Liu, and X. Fu, “Relaxation in nonconvex optimal control problems described by fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 409, no. 1, pp. 446–458, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. F. Punzo and G. Terrone, “On the Cauchy problem for a general fractional porous medium equation with variable density,” Nonlinear Analysis: Theory, Methods & Applications, vol. 98, pp. 27–47, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. D. R. Smart, Fixed Point Theorems, Cambridge University Press, 1980.
  19. A. Granas and J. Dugundji, Fixed Point Theory, Springer, New York, NY, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet