  We present an entirely microscopic formulation of viscoleasticity of a fluid
starting from the microscopic Stokes-Oldroyd B Model assuming instantaneous
hydrodynamic friction, and show that linearization leads to a form for the
frequency dependent viscosity that can be directly applied to the Langevin
equation. Interestingly, the calculated expression of viscosity can be directly
mapped to the Jeffreys' model which is essentially macroscopic in nature with
the bulk viscoelasticity of the fluid being characterized by a complex elastic
modulus G(\omega). Further, we demonstrate that the concerned Green's function
is same as that in an incompressible, low Reynold's number Newtonian fluid with
the simple incorporation of frequency dependence in the viscosity term. We
proceed to evaluate the trajectory of a free Brownian particle in a
viscoelastic environment using our formalism and calculate parameters such as
the power spectral density, the autocorrelation function and the mean-square
displacement, which we then extend to the particle confined in a harmonic
potential in the fluid.
