The inhomogeneity is introduced by a nonzero density gradient which separates the plasma into two different regions where plasma density are constant.The Alfvén waves,the phase mixing and the fast magnetosonic wave are excited by the boundary condition in inhomogeneous magnetized plasma.By using the Hall-magnetohydrodynamics(MHD)model,it is found that there are Alfvén waves in the homogeneous regions,while the phase mixing appears in the inhomogeneous region.The interesting result is that a fast magnetosonic wave is excited in a different direction which has a nonzero angle between the wave propagation direction and the direction of the background magnetic field.The dependence of the propagation direction of the excited fast magnetosonic wave and its strength of the magnetic field on the plasma parameters are given numerically.The results show that increasing both the driving frequency and the ratio of magnetic pressure to thermal pressure will increase the acceleration of the electrons.The electron acceleration also depends on the inhomogeneity parameters.