  In this paper we consider heterogeneous diffusion processes with the
power-law dependence of the diffusion coefficient on the position and
investigate the influence of external forces on the resulting anomalous
diffusion. The heterogeneous diffusion processes can yield subdiffusion as well
as superdiffusion, depending on the behavior of the diffusion coefficient. We
assume that not only the diffusion coefficient but also the external force has
a power-law dependence on the position. We obtain analytic expressions for the
transition probability in two cases: when the power-law exponent in the
external force is equal to 2eta-1, where 2eta is the power-law exponent in the
dependence of the diffusion coefficient on the position, and when the external
force has a linear dependence on the position. We found that the power-law
exponent in the dependence of the mean square displacement on time does not
depend on the external force, this force changes only the anomalous diffusion
coefficient. In addition, the external force having the power-law exponent
different from 2eta-1 limits the time interval where the anomalous diffusion
occurs. We expect that the results obtained in this paper may be relevant for a
more complete understanding of anomalous diffusion processes.

Statistical Mechanics