  In this paper, we study in Friedmann-Robertson-Walker universe the
interaction between the viscous generalized Chaplygin gas with $f(R,T)$
gravity, which is an arbitrary function of the Ricci scalar $R$ and the trace
$T$ of the energy-momentum tensor. Assuming that the contents of universe is
dominated by a generalized Chaplygin gas and dark energy, we obtained the
modified Friedmann equations and also the time dependent energy density and
pressure of dark energy due to the shear and bulk viscosities for three
interacting models depending on an input parameter $Q$. Within the simple form
of scale factor (power-law), we discuss the graphical representation of dark
energy density parameter and investigate the shear and bulk viscosities effects
on the accelerating expansion of the universe for each interacting model.
