Engineering with Computers

, Volume 35, Issue 1, pp 229–241 | Cite as

Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (MOL)

  • Saeed Kazem
  • Mehdi DehghanEmail author
Original Article


In this article, we apply the method of lines (MOL) for solving the time-fractional diffusion equations (TFDEs). The use of MOL yields a system of fractional differential equations with the initial value. The solution of this system could be obtained in the form of Mittag–Leffler matrix function. A direct method which computes the Mittag–Leffler matrix by applying its eigenvalues and eigenvectors analytically has been discussed. The direct approach has been applied on one-, two-, and three-dimensional TFDEs with Dirichlet, Neumann, and periodic boundary conditions as well.


Method of lines Time-fractional diffusion equations Mittag–Leffler function Matrix exponential function Tridiagonal matrix Dirichlet Neumann and periodic boundary conditions 

AMS subject classification:

65M20 65M06 



The authors are grateful to the reviewers for their comments and suggestions which have improved the paper.


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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran

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