  In this note we analyze a model for a unidirectional unsteady flow of a
viscous incompressible fluid with time dependent viscosity. A possible way to
take into account such behaviour is to introduce a memory formalism, including
thus the time dependent viscosity by using an integro-differential term and
therefore generalizing the classical equation of a Newtonian viscous fluid. A
possible useful choice, in this framework, is to use a rheology based on
stress/strain relation generalized by fractional calculus modelling. This is a
model that can be used in applied problems, taking into account a power law
time variability of the viscosity coefficient. We find analytic solutions of
initial value problems in an unbounded and bounded domain. Furthermore, we
discuss the explicit solution in a meaningful particular case.
