This study presented a new exact solution for anisotropic compact stellar objects within the framework of
𝑓(𝑅)=𝑅+𝛼𝑅2 gravity. In this context, the Durgapal-Fuloria metric potential has been employed to solve the field equation derived for 𝑓(𝑅) theory. Furthermore, we have derived the generalized Darmois-Israel junction condition necessary for seamlessly connecting the interior region to the Schwarzschild exterior metric across the boundary hypersurface of the star in the context of
𝑓(𝑅) gravity, and the interior solution is matched with the Schwarzschild exterior metric over the bounding surface of a compact star. These junction conditions stipulate that the pressure must not be zero at the boundary and should be proportional to the non-linear terms of 𝑓(𝑅) gravity, a crucial aspect often overlooked by many researchers when investigating compact stellar models. Additionally, we derived the values of these parameters by using observational data of various compact stars (CSs), namely Her X-1, SAX J1808.4-3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1416-2230. This approach enables us to investigate the comprehensive analysis of solutions numerically and graphically. We conducted various physical tests, including gradient of energy density and pressures, anisotropy, stability, equilibrium conditions, energy-density constraints, mass function, compactness, redshift, and adiabatic index, to assess the feasibility of our models. Our findings demonstrate the consistent behavior of our models provides a satisfactory physical situation as far as the observational results are confirmed.
