  We consider parabolic Schr\"odinger type equations associated to fractional
powers of uniformly elliptic 2m-order operators with constant coefficients.
Potentials and initial data are considered in suitable Morrey spaces. By means
of perturbation techniques we prove that several properties of the problem with
no potential are preserved. We also prove continuous dependence of solutions
with respect to perturbations. To carry out the analysis a general abstract
perturbation approach is developed, which broadens the results known in the
literature.
