710
Views
39
CrossRef citations to date
0
Altmetric
Section B

Numerical solution of time-fractional fourth-order partial differential equations

&
Pages 1496-1518 | Received 16 Jan 2014, Accepted 12 Jul 2014, Published online: 18 Aug 2014

References

  • M. Dehghan, Solution of a partial integro-differential equation arising from viscoelasticity, Int. J. Comput. Math. 83 (2006), pp. 123–129. doi: 10.1080/00207160500069847
  • A. Khan, I. Khan, and T. Aziz, Sextic spline solution for solving fourth-order parabolic partial differential equation, Int. J. Comput. Math. 82 (2005), pp. 871–879. doi: 10.1080/00207160512331331165
  • N.A. Khan, N.U. Khan, M. Ayaz, A. Mahmood, and N. Fatima, Numerical study of time-fractional fourth-order differential equations with variable coefficients, J. King Saud Univ. (Sci.) 23 (2011), pp. 91–98. doi: 10.1016/j.jksus.2010.06.012
  • W. Li and X. Da, Finite central difference/finite element approximations for parabolic integro-differential equations, Computing 90 (2010), pp. 89–111. doi: 10.1007/s00607-010-0105-0
  • Y. Lin and C. Xu, Finite difference/spectral approximations for time-fractional diffusion equation, J. Comput. Phys. 225 (2007), pp. 1533–1552. doi: 10.1016/j.jcp.2007.02.001
  • K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
  • K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
  • I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  • X.H. Yang, D. Xu, and H.X. Zhang, Quasi-wavelet based numerical method for fourth-order partial integro-differential equations with a weakly singular kernel, Int. J. Comput. Math. 88(15) (2011), pp. 3236–3254. doi: 10.1080/00207160.2011.587003
  • X.H. Yang, D. Xu, and H.X. Zhang, Crank-Nicolson/quasi-wavelets method for solving fourth order partial integro-differential equation with a weakly singular kernel, J. Comput. Phys. 234 (2013), pp. 317–329. doi: 10.1016/j.jcp.2012.09.037
  • H.X. Zhang and X. Han, Quasi-wavelet method for time-dependent fractional partial differential equation, Int. J. Comput. Math. (2013). doi.org/10.1080/00207160.2013.786050
  • H.X. Zhang, X. Han, and X.H. Yang, Quintic B-spline collocation method for fourth order partial integro-differential equations with a weakly singular kernel, Appl. Math. Comput. 219 (2013), pp. 6565–6575. doi: 10.1016/j.amc.2013.01.012

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.