About one method of approximate solution of the first boundary value problem for the fractional diffusion equation

This paper contains analytical and approximate solution of the one-dimensional fractional advection-diffusion equation in space. The solution is carried out by the method of separation of variables (Fourier method), the basis of the eigenfunctions of the system and of the biorthogonal problem is determined, and the eigenvalues for the basic equation are calculated. The method of estimating the accuracy of the approximate solution is considered. The results of calculations for concrete examples are given.