Numerical methods for the solution of partial differential equations of fractional order
Journal of Computational Physics
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Weighted average finite difference methods for fractional diffusion equations
Journal of Computational Physics
Numerical treatment of fractional heat equations
Applied Numerical Mathematics
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
Journal of Computational Physics
Numerical inversion of 2-D Laplace transforms applied to fractional diffusion equations
Applied Numerical Mathematics
Boundary particle method for Laplace transformed time fractional diffusion equations
Journal of Computational Physics
Numerical solution of distributed order fractional differential equations
Journal of Computational Physics
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A numerical method is presented for the solution of partial fractional differential equations (FDEs) arising in engineering applications and in general in mathematical physics. The solution procedure applies to both linear and nonlinear problems described by evolution type equations involving fractional time derivatives in bounded domains of arbitrary shape. The method is based on the concept of the analog equation, which in conjunction with the boundary element method (BEM) enables the spatial discretization and converts a partial FDE into a system of coupled ordinary multi-term FDEs. Then this system is solved using the numerical method for the solution of such equations developed recently by Katsikadelis. The method is illustrated by solving second order partial FDEs and its efficiency and accuracy is validated.