  The non-Markovian stochastic dynamics involving Levy flights and a potential
in the form of a harmonic and non-linear oscillator is discussed. The
subordination technique is applied and the memory effects, which are
nonhomogeneous, are taken into account by a position-dependent subordinator. In
the non-linear case, the asymptotic stationary states are found. The relaxation
pattern to the stationary state is derived for the quadratic potential: the
density decays like a linear combination of the Mittag-Leffler functions. It is
demonstrated that in the latter case the density distribution satisfies a
fractional Fokker-Planck equation. The densities for the non-linear oscillator
reveal a complex picture, qualitatively dependent on the potential strength,
and the relaxation pattern is exponential at large time.
