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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 789836, 7 pages
http://dx.doi.org/10.1155/2013/789836
Research Article

Positive Solutions of Fractional Differential Equation with -Laplacian Operator

College of Business Administration, Hunan University, Changsha, Hunan 410082, China

Received 27 November 2012; Accepted 5 February 2013

Academic Editor: Fuding Xie

Copyright © 2013 Teng Ren and Xiaochun Chen. 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. C. Almeida and J. Vicente, “Are interest rate options important for the assessment of interest rate risk?” Journal of Banking & Finance, vol. 33, pp. 1376–1387, 2009.
  2. X. Zhang and L. Liu, “Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator,” Journal of Mathematical Analysis and Applications, vol. 336, no. 2, pp. 1414–1423, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. Wang, H. Xiang, and Z. Liu, “Upper and lower solutions method for a class of singular fractional boundary value problems with p-Laplacian operator,” Abstract and Applied Analysis, vol. 2010, Article ID 971824, 12 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  4. D.-X. Ma and X.-Z. Yang, “Upper and lower solution method for fourth-order four-point boundary value problems,” Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 543–551, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Chen, W. Ni, and C. Wang, “Positive solution of fourth order ordinary differential equation with four-point boundary conditions,” Applied Mathematics Letters, vol. 19, no. 2, pp. 161–168, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Z. Bai and H. Lv, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. K. S. Miller and B. Ross, Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, NY, USA, 1993. View at MathSciNet
  8. M. Jia, X. Liu, and X. Gu, “Uniqueness and asymptotic behavior of positive solutions for a fractional-order integral boundary value problem,” Abstract and Applied Analysis, vol. 2012, Article ID 294694, 21 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Jia, X. Zhang, and X. Gu, “Nontrivial solutions for a higher fractional differential equation with fractional multi-point boundary conditions,” Boundary Value Problems, vol. 2012, article 70, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. X. Zhang and Y. Han, “Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations,” Applied Mathematics Letters, vol. 25, no. 3, pp. 555–560, 2012.
  11. X. Zhang, L. Liu, and Y. Wu, “The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives,” Applied Mathematics and Computation, vol. 218, no. 17, pp. 8526–8536, 2012.
  12. X. Zhang, L. Liu, and Y. Wu, “The uniqueness of positive solution for a singular fractional differential system involving derivatives,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, pp. 1400–1409, 2013.
  13. X. Zhang, L. Liu, B. Wiwatanapataphee, and Y. Wu, “Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives,” Abstract and Applied Analysis, vol. 2012, Article ID 512127, 16 pages, 2012. View at Publisher · View at Google Scholar
  14. X. Zhang, L. Liu, and Y. Wu, “Existence results formultiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1420–1433, 2012.
  15. X. Zhang, L. Liu, Y. Wu, and Y. Lu, “The iterative solutions of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 219, no. 9, pp. 4680–4691, 2013.
  16. I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999. View at MathSciNet
  17. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993. View at MathSciNet