Table of Contents Author Guidelines Submit a Manuscript
Corrigendum

A corrigendum for this article has been published. To view the corrigendum, please click here.

Abstract and Applied Analysis
Volume 2014, Article ID 162896, 7 pages
http://dx.doi.org/10.1155/2014/162896
Research Article

Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials

1Department of Mathematics, Aligoudarz Branch, Islamic Azad University, Aligoudarz, Iran
2Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
3Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa

Received 26 November 2013; Accepted 12 February 2014; Published 18 March 2014

Academic Editor: Hossein Jafari

Copyright © 2014 Emran Tohidi 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. A. E. M. El-Mesiry, A. M. A. El-Sayed, and H. A. A. El-Saka, “Numerical methods for multi-term fractional (arbitrary) orders differential equations,” Applied Mathematics and Computation, vol. 160, no. 3, pp. 683–699, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, New York, NY, USA, 2006. View at MathSciNet
  3. 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
  4. I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1999. View at MathSciNet
  5. S. A. El-Wakil, A. Elhanbaly, and M. A. Abdou, “Adomian decomposition method for solving fractional nonlinear differential equations,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 313–324, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. Das, “Analytical solution of a fractional diffusion equation by variational iteration method,” Computers & Mathematics with Applications, vol. 57, no. 3, pp. 483–487, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. V. S. Erturk, S. Momani, and Z. Odibat, “Application of generalized differential transform method to multi-order fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1642–1654, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. M. Meerschaert and C. Tadjeran, “Finite difference approximations for two-sided space-fractional partial differential equations,” Applied Numerical Mathematics, vol. 56, no. 1, pp. 80–90, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Z. M. Odibat and N. T. Shawagfeh, “Generalized Taylor's formula,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 286–293, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Gülsu, B. Gürbüz, Y. Öztürk, and M. Sezer, “Laguerre polynomial approach for solving linear delay difference equations,” Applied Mathematics and Computation, vol. 217, no. 15, pp. 6765–6776, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. O. R. N. Samadi and E. Tohidi, “The spectral method for solving systems of Volterra integral equations,” Journal of Applied Mathematics and Computing, vol. 40, no. 1-2, pp. 477–497, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. E. Tohidi, F. Soleymani, and A. Kilicman, “Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems,” Abstract and Applied Analysis, vol. 2013, Article ID 535979, 9 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. F. Toutounian, E. Tohidi, and A. Kilicman, “Fourier operational matrices of differentiation and transmission: introduction and applications,” Abstract and Applied Analysis, vol. 2013, Article ID 198926, 11 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. S. Yalçinbaş, M. Aynigül, and M. Sezer, “A collocation method using Hermite polynomials for approximate solution of pantograph equations,” Journal of the Franklin Institute, vol. 348, no. 6, pp. 1128–1139, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. Yüzbaşı, “A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differential-difference equations,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 1691–1705, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. E. Tohidi and A. Kılıçman, “A collocation method based on the Bernoulli operational matrix for solving nonlinear BVPs which arise from the problems in calculus of variation,” Mathematical Problems in Engineering, vol. 2013, Article ID 757206, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. E. Tohidi, Kh. Erfani, M. Gachpazan, and S. Shateyi, “A new Tau method for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation,” Journal of Applied Mathematics, vol. 2013, Article ID 850170, 9 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. F. Toutounian, E. Tohidi, and S. Shateyi, “A collocation method based on the Bernoulli operational matrix for solving high-order linear complex differential equations in a rectangular domain,” Abstract and Applied Analysis, vol. 2013, Article ID 823098, 12 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. A. Saadatmandi and M. Dehghan, “A Legendre collocation method for fractional integro-differential equations,” Journal of Vibration and Control, vol. 17, no. 13, pp. 2050–2058, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. H. Saeedi and M. M. Moghadam, “Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1216–1226, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet