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