Observational Constraints and Cosmological Dynamics of Interacting Fractional Holographic Dark Energy in Light of DESI DR2

Based on the fractional entropy originating from fractional quantum mechanics, the fractional holographic dark energy (FHDE) model has been proposed. In this paper, we consider an interaction between the pressureless matter and FHDE and analyze three different interacting FHDE models. Combining the latest observational data including SNIa, OHD, BAO, and CMB, we estimate the model parameters and find that the interaction forms $Q=\gamma H{\rho }_{de}$ and $Q=\beta H{\rho }_m+\gamma H{\rho }_{de}$ show some preference from the observational data. Using phase space analysis, we further find that only interacting FHDE model with $Q=\beta H{\rho }_m+\gamma H{\rho }_{de}$ can describe the full evolutionary history of the universe. The statefinder diagnostic pair reveals that this model deviates from the $\mathrm{\Lambda }$CDM model but converges to the $\mathrm{\Lambda }$CDM fixed point and the de Sitter expansion fixed point in the future. Finally, we analyze the evolution of cosmological parameters and demonstrate that this model can drive the late time acceleration of the universe.