## Variational formulation for the stationary fractional advection dispersion equation.(English)Zbl 1095.65118

This paper deals with the Galerkin approximation to the steady state fractional advection dispersion equation: $$-Da(p_0D_x^{-\beta}+q_x D_1^{-\beta})Du+b(x)Du+c (x)u=f$$, where $$D$$ represents a single spatial derivative, and $$_0D_x^{-\beta}$$, $$_xD_1^{-\beta}$$ represent left and right fractional integral operators, with $$0\leq\beta<1$$, and $$0\leq p$$, $$q\leq 1$$, satisfying $$p+q=1$$. Convergence results are derived. Numerical calculations for piecewise linear polynomials are presented.

### MSC:

 65R20 Numerical methods for integral equations 26A33 Fractional derivatives and integrals 45K05 Integro-partial differential equations
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### References:

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