  We derive the fractional master equation with space dependent anomalous
exponent. We analyze the asymptotic behavior of corresponding lattice model
both analytically and by Monte Carlo simulation. We show that the subdiffusive
fractional equations with constant anomalous exponent $\mu $ in a bounded
domain $[ 0,L]$ are not structurally stable with respect to the non-homogeneous
variations of parameter $\mu $. In particular, the Gibbs-Boltzmann distribution
is no longer the stationary solution of the fractional Fokker-Planck equation
whatever the space variation of the exponent might be. We analyze the random
distribution of $% \mu$ in space and find that in the long time limit, the
probability distribution is highly intermediate in space and the behavior is
completely dominated by very unlikely events.
