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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 615707, 6 pages
http://dx.doi.org/10.1155/2013/615707
Research Article

Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model

1Department of Electrical Engineering, North China Electric Power University, Baoding 071003, China
2Department of Management and Economic, North China Electric Power University, Baoding 071003, China
3School of Land Science and Technology, China University of Geosciences, Beijing 100083, China
4Institute of Finance and Banking, Chinese Academy of Social Sciences, Beijing, China

Received 13 May 2013; Accepted 1 July 2013

Academic Editor: Yonghong Wu

Copyright © 2013 Rui Li 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. J. R. L. Webb and G. Infante, “Positive solutions of nonlocal boundary value problems involving integral conditions,” Nonlinear Differential Equations and Applications, vol. 15, no. 1-2, pp. 45–67, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. R. L. Webb and G. Infante, “Positive solutions of nonlocal boundary value problems: a unified approach,” Journal of the London Mathematical Society, vol. 74, no. 3, pp. 673–693, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. R. L. Webb, “Nonlocal conjugate type boundary value problems of higher order,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 5-6, pp. 1933–1940, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. X. Hao, L. Liu, Y. Wu, and Q. Sun, “Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 73, no. 6, pp. 1653–1662, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Tao, M. Fu, and R. Qian, “Positive solutions for fractional differential equations from real estate asset securitization via new fixed point theorem,” Abstract and Applied Analysis, vol. 2012, Article ID 842358, 11 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. 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.
  8. X. Zhang, L. Liu, and Y. Wu, “Multiple positive solutions of a singular fractional differential equation with negatively perturbed term,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 1263–1274, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. W. Wang and L. Huang, “Existence of positive solution for semipositone fractional differential equations involving Riemann-Stieltjes integral conditions,” Abstract and Applied Analysis, vol. 2012, Article ID 723507, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. X. Zhang, L. Liu, and Y. Wu, “Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 1420–1433, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  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 · View at Zentralblatt MATH · View at MathSciNet
  14. 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.
  15. J. Harjani and K. Sadarangani, “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 7-8, pp. 3403–3410, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  17. I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, vol. 198, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  18. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier, Amsterdam, The Netherlands, 2006. View at MathSciNet
  19. Z. Bai and H. Lü, “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
  20. J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. J. Caballero, J. Harjani, and K. Sadarangani, “On existence and uniqueness of positive solutions to a class of fractional boundary value problems,” Boundary Value Problems, vol. 2011, 25 pages, 2011. View at MathSciNet