Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Finite difference approximations for fractional advection-dispersion flow equations
Journal of Computational and Applied Mathematics
Weighted average finite difference methods for fractional diffusion equations
Journal of Computational Physics
Finite difference approximations for two-sided space-fractional partial differential equations
Applied Numerical Mathematics
Numerical solution of two-sided space-fractional wave equation using finite difference method
Journal of Computational and Applied Mathematics
A radial basis functions method for fractional diffusion equations
Journal of Computational Physics
A high order schema for the numerical solution of the fractional ordinary differential equations
Journal of Computational Physics
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In this article, an accurate numerical approach is introduced. In this approach we mixed between the fractional finite difference method and the restrictive Taylor approximation (RTA). The proposed method is implemented to solve numerically the perturbed fractional partial differential equations (FPDEs). Special attention is given to study the stability and consistency of the method by means of Gerschgorin theorem and using the stability matrix analysis. Two numerical examples are given and compared with the exact solution.