The observed late-time acceleration of the universe remains one of the most profound puzzles in modern cosmology. While the standard approach attributes this acceleration to an unknown dark energy component within the framework of General Relativity, modified gravity theories-particularly f(R) gravity-have emerged as compelling alternatives that do not invoke exotic matter fields. In this work, we propose a new f(R) gravity model of the form \(f(R)=R+\frac{\gamma {R}^\frac{{1}}{n}}{1+\mu {R}^\frac{{1}}{n}}\) where γ, μ and n are model parameters. For small curvature, this model effectively behaves as \(f(R)\approx R+\gamma {R}^\frac{{1}}{n}\) , allowing the curvature modification to mimic a dynamically evolving dark energy component with \({\rho }_{DE}\propto {a}^{-\frac{2}{np}}\) , which drives late-time acceleration, particularly \({\rho }_{DE}\propto {a}^{-1}\) for \(np=2\) , by assuming a power-law behaviour for scale factor. At high curvature, the correction term is suppressed, ensuring the model closely approximates General Relativity and enables a chameleon-like screening mechanism that satisfies local gravity constraints. We derive the modified Friedmann equations in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) background and analyse the cosmological dynamics driven by the proposed model. Through analytical techniques, we investigate the conditions under which the model produces late cosmic acceleration without introducing a cosmological constant. We also examine the behaviour of the effective equation of state and demonstrate the physical viability of the model by comparing its predictions with current observational data and applying various stability tests, including a thermodynamic analysis. Our findings suggest that the proposed model is a viable alternative to dark energy, consistent with both cosmological and solar system constraints.
