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Approximate solution of the fractional advection-dispersion equation. (English) Zbl 1210.65168
The solution of the advection-dispersion equation of fractional order $$\frac{\partial^{\alpha}u(x,t)}{\partial t^{\alpha}}+ v(x,t)D_{x}^{\nu}u(x,t)-k(x,t)D_{x}^{\beta}u(x,t)=F(x,t)$$ with homogeneous initial and boundary conditions is presented in the form of Fourier series. The approximate solution is obtained by truncating this series.

MSC:
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
42C10Fourier series in special orthogonal functions
35L50First order hyperbolic systems, boundary value problems
35R11Fractional partial differential equations
35C10Series solutions of PDE
46E22Hilbert spaces with reproducing kernels
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References:
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