Table of Contents
ISRN Mathematical Analysis
Volume 2011, Article ID 468346, 14 pages
http://dx.doi.org/10.5402/2011/468346
Research Article

Existence Results for a Coupled System of Nonlinear Fractional Differential Equation with Four-Point Boundary Conditions

1Faculty of Education Al-Arish, Suez Canal University, Ismailia 41522, Egypt
2Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt

Received 30 August 2011; Accepted 20 October 2011

Academic Editor: J.-L. Wu

Copyright © 2011 M. Gaber and M. G. Brikaa. 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. A. Babakhani and V. D. Gejji, β€œExistence of positive solutions of nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 278, no. 2, pp. 434–442, 2003. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  2. Z. Bai and H. Lu, β€œPositive 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 Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  3. M. El-Shahed and J. J. Nieto, β€œNontrivial solutions for a nonlinear multi-point boundary value problem of fractional order,” Computers & Mathematics with Applications, vol. 59, no. 11, pp. 3438–3443, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  4. T. Jankowski, β€œPositive solutions to second order four-point boundary value problems for impulsive differential equations,” Applied Mathematics and Computation, vol. 202, no. 2, pp. 550–561, 2008. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  5. 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, Amsterdam, The Netherlands, 2006.
  6. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
  7. I. Podlubny, β€œGeometric and physical interpretation of fractional integration and fractional differentiation,” Fractional Calculus & Applied Analysis, vol. 5, no. 4, pp. 367–386, 2002. View at Google Scholar Β· View at Zentralblatt MATH
  8. S. Zhang, β€œPositive solution for boundary value problem of nonlinear frctional differential equations,” Electronic Journal of Differential Equations, vol. 2006, no. 36, pp. 1–12, 2006. View at Google Scholar
  9. Y. Chen and H.-L. An, β€œNumerical solution of coupled Burgers equations with time and space fractional derivatives,” Applied Mathematics and Computation, vol. 200, no. 1, pp. 87–95, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  10. V. Gafiychuk, B. Datsko, V. Meleshko, and D. Blackmore, β€œAnalysis of the solutions of coupled nonlinear fractional reaction-diffusion equations,” Chaos, Solitons and Fractals, vol. 41, no. 3, pp. 1095–1104, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  11. X. Su, β€œBoundary value problem for a coupled system of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 22, no. 1, pp. 64–69, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  12. C. Z. Bai and J. X. Fang, β€œThe existence of a positive solution for a singular coupled system of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 150, no. 3, pp. 611–621, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  13. B. Ahmad and J. J. Nieto, β€œExistence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions,” Computers & Mathematics with Applications, vol. 58, no. 9, pp. 1838–1843, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet