About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 813903, 5 pages
http://dx.doi.org/10.1155/2013/813903
Research Article

Nonlocal Integrodifferential Boundary Value Problem for Nonlinear Fractional Differential Equations on an Unbounded Domain

1School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
3Department of Mathematics, Texas A and M University, Kingsville, TX 78363-8202, USA

Received 8 May 2013; Accepted 10 June 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 Lihong Zhang 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. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999. View at Zentralblatt MATH · View at MathSciNet
  2. G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2008. View at Zentralblatt MATH · View at MathSciNet
  3. R. L. Magin, Fractional Calculus in Bioengineering, Begell House, Redding, Conn, USA, 2006.
  4. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. P. Lazarević and A. M. Spasić, “Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 475–481, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. D. Ramírez and A. S. Vatsala, “Monotone iterative technique for fractional differential equations with periodic boundary conditions,” Opuscula Mathematica, vol. 29, no. 3, pp. 289–304, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Zhang, “Existence results of positive solutions to boundary value problem for fractional differential equation,” Positivity, vol. 13, no. 3, pp. 583–599, 2009.
  10. B. Ahmad and J. J. Nieto, “Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2009, Article ID 494720, 9 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z. Wei, Q. Li, and J. Che, “Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative,” Journal of Mathematical Analysis and Applications, vol. 367, no. 1, pp. 260–272, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. B. Ahmad and S. K. Ntouyas, “A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order,” Electronic Journal of Qualitative Theory of Differential Equations, no. 22, pp. 1–15, 2011. View at MathSciNet
  13. Y. Zhao, S. Sun, Z. Han, and M. Zhang, “Positive solutions for boundary value problems of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 217, no. 16, pp. 6950–6958, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. 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. View at MathSciNet
  15. G. Wang, “Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments,” Journal of Computational and Applied Mathematics, vol. 236, no. 9, pp. 2425–2430, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. Wang, D. Baleanu, and L. Zhang, “Monotone iterative method for a class of nonlinear fractional differential equations,” Fractional Calculus and Applied Analysis, vol. 15, no. 2, pp. 244–252, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  17. A. Babakhani, “Positive solutions for system of nonlinear fractional differential equations in two dimensions with delay,” Abstract and Applied Analysis, vol. 2010, Article ID 536317, 16 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. V. Gafiychuk, B. Datsko, V. Meleshko, and D. Blackmore, “Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations,” Chaos, Solitons & Fractals, vol. 41, no. 3, pp. 1095–1104, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. A. Arara, M. Benchohra, N. Hamidi, and J. J. Nieto, “Fractional order differential equations on an unbounded domain,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 72, no. 2, pp. 580–586, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. X. Zhao and W. Ge, “Unbounded solutions for a fractional boundary value problems on the infinite interval,” Acta Applicandae Mathematicae, vol. 109, no. 2, pp. 495–505, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Liang and J. Zhang, “Existence of three positive solutions of m-point boundary value problems for some nonlinear fractional differential equations on an infinite interval,” Computers & Mathematics with Applications, vol. 61, no. 11, pp. 3343–3354, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  22. X. Su, “Solutions to boundary value problem of fractional order on unbounded domains in a Banach space,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 74, no. 8, pp. 2844–2852, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. S. Liang and J. Zhang, “Existence of multiple positive solutions for m-point fractional boundary value problems on an infinite interval,” Mathematical and Computer Modelling, vol. 54, no. 5-6, pp. 1334–1346, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  24. G. Wang, B. Ahmad, and L. Zhang, “A coupled system of nonlinear fractional differential equations with multipoint fractional boundary conditions on an unbounded domain,” Abstract and Applied Analysis, vol. 2012, Article ID 248709, 11 pages, 2012. View at Zentralblatt MATH · View at MathSciNet
  25. Y. Liu, “Existence and uniqueness of solutions for initial value problems of multi-order fractional differential equations on the half lines,” Scientia Sinica Mathematica, vol. 42, no. 7, pp. 735–756, 2012. View at Publisher · View at Google Scholar
  26. L. Zhang, B. Ahmad, G. Wang, and R. P. Agarwal, “Nonlinear fractional integro-differential equations on unbounded domains in a Banach space,” Journal of Computational and Applied Mathematics, vol. 249, pp. 51–56, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  27. R. P. Agarwal, M. Meehan, and D. O'Regan, Fixed Point Theory and Applications, vol. 141, Cambridge University Press, Cambridge, UK, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  28. Y. Liu, “Existence and unboundedness of positive solutions for singular boundary value problems on half-line,” Applied Mathematics and Computation, vol. 144, no. 2-3, pp. 543–556, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet