Holographic-fractional model constrained with recent datasamples and DESI data

Abstract This paper aims to extend fractional theories by incorporating the holographic concept to address the challenge of α &gt; 2, a range which is used to obtain late-time acceleration, despite the fact that the standard theoretical framework of fractional calculus is typically constrained to 1 ≤ α ≤ 2. Additionally, we seek to alleviate the discrepancy in the estimated age of the Universe ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>33.61</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4.511</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>3.411</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> Gyrs), which significantly exceeds standard estimations. Thus, we begin our analysis setting α = 1, which corresponds to a fully fractional theory extended with holographic terms, and constrain it using recent observational datasets—including cosmic chronometers, type Ia supernovae, quasars, hydrogen II galaxies, baryon acoustic oscillations from the Dark Energy Spectroscopic Instrument, and cosmic microwave background radiation. Our first result is that the Friedmann equation we derive is similar to the Dvali-Gabadadze-Porrati (DGP) Friedmann equation from braneworld models. Moreover, late-time acceleration is obtained in the region expected for fractional calculus, and constraints suggest values of the free parameters consistent with the standard model, including the age of the Universe ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>U</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>13.86</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.015</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.015</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> Gyrs) for the combined samples. Further cosmographic and statefinder analyses indicate a dynamical dark energy evolving toward an asymptotic cosmological constant behavior. However, a statistical comparison based on the Akaike Information Criterion still favors the standard model of cosmology in the context of the datasets considered.