Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 919052, 5 pages
http://dx.doi.org/10.1155/2014/919052
Research Article

Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order

1Department of Mathematical Sciences, University of South Africa, Pretoria 0003, South Africa
2Department of Mathematics, University of Mazandaran, Babolsar 47416-95447, Iran
3Department of Mathematics and Statistics, Faculty of Science, Tshwane University of Technology, Arcadia Campus, Building 2-117, Nelson Mandela Drive, Pretoria 0001, South Africa

Received 6 March 2014; Accepted 7 May 2014; Published 15 June 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Hossein Jafari 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. H. Jafari, An Introduction To Fractional Differential Equations, Mazandaran University Press, 2013, (Persian).
  2. H. Jafari, K. Sayevand, H. Tajadodi, and D. Baleanu, “Homotopy analysis method for solving Abel differential equation of fractional order,” Central European Journal of Physics, vol. 11, no. 10, pp. 1523–1527, 2013. View at Google Scholar
  3. S. Kumar and O. P. Singh, “Numerical inversion of the abel integral equation using homotopy perturbation method,” Zeitschrift Fur Naturforschung, vol. 65, pp. 677–682, 2010. View at Google Scholar
  4. A.-M. Wazwaz, “Adomian decomposition method for a reliable treatment of the Bratu-type equations,” Applied Mathematics and Computation, vol. 166, no. 3, pp. 652–663, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. M. Wazwaz, “A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems,” Computers & Mathematics with Applications, vol. 41, no. 10-11, pp. 1237–1244, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Adomian and R. Rach, “Analytic solution of nonlinear boundary value problems in several dimensions by decomposition,” Journal of Mathematical Analysis and Applications, vol. 174, no. 1, pp. 118–137, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  7. G. Adomian, M. Elrod, and R. Rach, “A new approach to boundary value equations and application to a generalization of Airy's equation,” Journal of Mathematical Analysis and Applications, vol. 140, no. 2, pp. 554–568, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. O. P. Agrawal, “Solution for a fractional diffusion-wave equation defined in a bounded domain,” Nonlinear Dynamics, vol. 29, no. 1–4, pp. 145–155, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. R. Metzler and J. Klafter, “Boundary value problems for fractional diffusion equations,” Physica A. Statistical Mechanics and Its Applications, vol. 278, no. 1-2, pp. 107–125, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  10. 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
  11. H. Jafari and V. Daftardar-Gejji, “Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method,” Applied Mathematics and Computation, vol. 180, no. 2, pp. 700–706, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  14. N. T. Shawagfeh, “Analytical approximate solutions for nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 131, no. 2-3, pp. 517–529, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Jafari and S. Momani, “Solving fractional diffusion and wave equations by modified homotopy perturbation method,” Physics Letters A, vol. 370, no. 5-6, pp. 388–396, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. H. Jafari, S. Ghasempoor, and C. M. Khalique, “A comparison between Adomian's polynomials and He's polynomials for nonlinear functional equations,” Mathematical Problems in Engineering, vol. 2013, Article ID 943232, 4 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z. M. Odibat, “A new modification of the homotopy perturbation method for linear and nonlinear operators,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 746–753, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet