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The fundamental and numerical solutions of the Riesz space-fractional reaction-dispersion equation. (English) Zbl 1179.35029
An analog of a linear diffusion equation in \(\mathbb R\) with drift is considered wherein the Laplacian is replaced by a fractional derivative of order \(\beta \in (1, 2]\). Its fundamental solution is obtained by Laplace-Fourier transform method. An explicit finite difference approximation is proposed and its stability and convergence is analyzed. A numerical example is given.

MSC:
35A35 Theoretical approximation in context of PDEs
35K57 Reaction-diffusion equations
35A08 Fundamental solutions to PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
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