  This paper examines the general formalism and applications of isotropic as
well as anisotropic polytropic stars in curvature-matter coupled gravity. For
this purpose, we consider static spherical and Schwarzschild spacetimes in the
interior and exterior regions, respectively. We use two polytropic equations of
state to obtain physically viable solutions of the field equations. The
hydrostatic equilibrium and Lane-Emden equations are developed for both
isotropic as well as anisotropic cases. We study the effects of anisotropic
pressure on the stellar structure. Moreover, we graphically inspect the
physical behavior of isotropic as well as anisotropic polytropes through energy
conditions and stability criterion. Finally, we discuss Tolman mass to explore
some characteristics of the models. It is concluded that more viable and stable
polytropes are found in this theory as compared to general relativity.
