Observational Constraints on Fractional Holographic Dark Energy in the Light of DESI DR2

Based on the fractional entropy from fractional quantum mechanics, fractional holographic dark energy (FHDE) has been proposed with the Hubble horizon as the IR cutoff (FHDEH). We extend this framework by adopting the future event horizon and the particle horizon as the IR cutoff, proposing the FHDEF and FHDEP models. Using the SN+OHD+DESI DR2 dataset to constrain these models, we find that all three models provide a marginally lower χ^2_min compared to ΛCDM but without significant preference according to AIC and BIC. When CMB distance priors are included, the FHDEH and FHDEP models are strongly ruled out. We further analyze the cosmological evolution for these models, and find that only the FHDEF model predicts nearly identical evolutions of Ω_m and Ω_de to those of the ΛCDM model across cosmic history, but its deceleration parameter q deviate from the ΛCDM model in the future, indicating richer late time dynamics beyond the standard ΛCDM cosmology.