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Mathematical Problems in Engineering
Volume 2015, Article ID 258265, 13 pages
http://dx.doi.org/10.1155/2015/258265
Review Article

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

1College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
2Science and Technology on Space Physics Laboratory, Beijing 100076, China
3School of Computer Science, National University of Defense Technology, Changsha 410073, China
4Department of Engineering Science, University of Oxford, Oxford OX2 0ES, UK

Received 13 June 2014; Revised 6 August 2014; Accepted 9 September 2014

Academic Editor: Guido Maione

Copyright © 2015 Chunye Gong 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.

Citations to this Article [5 citations]

The following is the list of published articles that have cited the current article.

  • Qinglin Wang, Chunye Gong, Xiantuo Tang, Guitao Fu, Jie Liu, and Zuocheng Xing, “An efficient parallel algorithm for Caputo fractional reaction-diffusion equation with implicit finite-difference method,” Advances in Difference Equations, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • Daliang Su, Weimin Bao, Jie Liu, and Chunye Gong, “An efficient simulation of the fractional chaotic system and its synchronization,” Journal of the Franklin Institute, 2016. View at Publisher · View at Google Scholar
  • G. Casas, A. Ferrer, and E. Oñate, “Approximating the Basset force by optimizing the method of van Hinsberg et al.,” Journal of Computational Physics, 2017. View at Publisher · View at Google Scholar
  • Hong Fang, Chunye Gong, Caihui Yu, Changwan Min, Xing Zhang, Jie Liu, and Liquan Xiao, “Efficient mesh deformation based on Cartesian background mesh,” Computers & Mathematics with Applications, vol. 73, no. 1, pp. 71–86, 2017. View at Publisher · View at Google Scholar
  • Chunye Gong, Weimin Bao, and Jie Liu, “A piecewise memory principle for fractional derivatives,” Fractional Calculus and Applied Analysis, vol. 20, no. 4, 2017. View at Publisher · View at Google Scholar