The modeling of astrophysical compact objects has recently attracted significant interest of the research community to understand their stable internal structures. In particular, the addition of dark energy as another source of matter configuration in the interiors of such stars has elevated the focus on their theoretical development. In this study, we present a ne model of static, spherically symmetric, and anisotropic compact stars within the framework of f(R) modified theories. The stellar structure is described by a two-fluid system consisting of ordinary matter and dark energy. We develop the analytical solutions to the governing modified field equations using the well-known Finch-Skea ansatz for the metric potentials, coupled with a linear equation of state for the dark energy component. The model parameters, including the metric ansatz, are determined via smooth matching conditions at the boundary between the interior and exterior spacetime regions. To demonstrate the physical viability of the model, we apply our formulation to the compact star 4U 1538-52, utilizing the stable and widely studied gravity model. We analyze an extensive investigation of the physical features, including the behavior of metric equations, matter variables, energy conditions, and stability criteria. In addition, we evaluate the evolution of the mass function, surface redshift, and compactness factor of the considered compact star candidates. The results confirm the stability, feasibility, and physical impact of the constructed solutions along with presenting additional insight into the interplay between dark energy structures and modified gravity within astrophysical circumstances. Graphical representations of key parameters enhance the clarity of our findings. The results demonstrate that our model is physically acceptable and stable in f(R) gravity.
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