This study develops a framework for deriving anisotropic solutions for compact spherical objects in the framework of f(Formula: see text) gravity. The approach employs the extended gravitational decoupling method. Anisotropy is introduced into the model by coupling a new source term to the original perfect fluid distribution, with a dimensionless decoupling parameter controlling the interaction. This methodology involves a transformation of the temporal and radial metric potentials, which subsequently decouples the system of field equations into two distinct sets. The first system is solved using the well-established Finch-Skea metric, known for its non-singular properties. The unknowns in the second system are then determined by applying appropriate constraints. We analyze the influence of the decoupling parameter on key physical properties to assess the viability of the resulting solutions. A comprehensive stability analysis for each solution is performed using the causality conditions derived from the sound speed method and the stability evaluation through adiabatic index. We find that solution I is presented only for mathematical completeness and not claimed to be physically viable and solution II remains feasible and stable in this framework for various decoupling parameter values.
Gul et al. (Fri,) studied this question.