Semi-analytical solution for time-fractional diffusion equation based on finite difference method of lines (MOL)
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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.
KeywordsMethod 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.
- 8.Euler L (1730) Memoire dans le tome V des Comment. Saint Petersberg Annees, 55Google Scholar
- 21.Mitchell AR, Griffiths DF (1980) The finite diffrerence method in partial differential equations. John Wiley, New YorkGoogle Scholar
- 25.Podlubny I, Kacenak M (2005) Mittag-Leffler function; calculates the Mittag-Leffler function with desired accuracy , MATLAB Central File Exchange, File ID 8735, mlf. mGoogle Scholar