Approximate solution of the fractional advection-dispersion equation (Q615100)

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.