f(R) gravity is an extension of Einstein's General Relativity derived from relaxing the hypothesis that the Hilbert-Einstein action for the gravitational field is strictly linear in the Ricci curvature scalar R and explains the late-time cosmic acceleration of the Universe. We investigate the spatially homogeneous and isotropic Friedmann-Robertson-Walker (FRW) line element filled with two fluids, with the first being pressureless matter and the second being the Renyi holographic dark energy (RHDE) in this study. In this scenario, the Hubble horizon H acts as an Infrared (IR) cutoff. In this regard, the effects of IR cutoff with the Hubble horizon on the traits of RHDE models have been researched. The volumetric power law expansion and the two models of f(R) i.e. f(R)=R+bRm and f(R)=R−μ4R are taken into consideration for the solution of the field equations. The estimated model parameter values that would best fit and work with current observational datasets. This estimation uses 1048 points from the Pantheon supernovae datasets and 30 points from the Hubble datasets. The likelihood function and Bayesian analysis are integrated with the Markov Chain Monte Carlo (MCMC) method at the 1 σ and 2 σ confidence levels. It is crucial to remember that f(R) is a rising function ofR, demonstrating the model's plausibility. For both models, the equation of state (EoS) value is close to a Quintessence zone. The model behaves in a ΛCDM (ΛCold Dark Matter) like manner, as shown by the fact that the statefinder diagnostic pair falls to(r=1,s=0). The Om(z) parameter shows a discrète behaviour.