ABSTRACT
In this review paper, we are mainly concerned with the finite difference methods, the Galerkin finite element methods, and the spectral methods for fractional partial differential equations (FPDEs), which are divided into the time-fractional, space-fractional, and space-time-fractional partial differential equations (PDEs). Besides, fast algorithms for the FPDEs are included in order to stimulate more efficient algorithms for high-dimensional FPDEs.
Acknowledgments
The authors wish to thank Professor Abdul Q. M. Khaliq, Editor-in-Chief of International Journal Computer Mathematics for his cordial invitation. The authors are also grateful to Professor Khaliq and the referees for the valuable comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.