  The aim of this work is to devise and analyse an accurate numerical scheme to
solve Erd\'elyi-Kober fractional diffusion equation. This solution can be
thought as the marginal pdf of the stochastic process called the generalized
grey Brownian motion (ggBm). The ggBm includes some well-known stochastic
processes: Brownian motion, fractional Brownian motion and grey Brownian
motion. To obtain convergent numerical scheme we transform the fractional
diffusion equation into its weak form and apply the discretization of the
Erd\'elyi-Kober fractional derivative. We prove the stability of the solution
of the semi-discrete problem and its convergence to the exact solution. Due to
the singular in time term appearing in the main equation the proposed method
converges slower than first order. Finally, we provide the numerical analysis
of the full-discrete problem using orthogonal expansion in terms of Hermite
functions.
