  Pseudo-differential operator equations with parameter are studied. Uniform
separability properties and resolvent estimates are obtained in terms of
fractional derivatives. Moreover, maximal regularity properties of the
pseudo-differential abstract parabolic equation are established. Particularly,
it is proven that the operators generated by these pseudo-differential
equations are positive and aso are generators of analytic semigroups. As an
application, the anisotropic parameter dependent pseudo-differential equations
and the system of pseudo-differential equations are studied
