To investigate the effects of fractional order (), nanoparticle volume fraction (), magnetic field strength (), and Brinkman permeability () on both flow and heat transfer characteristics, a detailed parametric and statistical analysis is conducted. The statistical regression analysis shows that the volume fraction of nanoparticles and temperature have a strong positive correlation (coefficient = 0.94, p = 0.021) indicating that Mo2C MXene is an excellent heat absorption. On the other hand, the fractional parameter α has a strong negative effect on temperature field (coefficient = − 0.086, p < 0.001), which emphasizes its importance in describing the effects of thermal memory. The findings also indicate that, although MXene nanoparticles significantly increase thermal transport, an augmentation in magnetic field strength and Brinkman resistance cause a resistive Lorentz force and frictional drag, respectively, to prevent fluid flow. These results are physically informative about non-Fourier heat transfer in MXene-based nanofluids as well as offer invaluable information to developing high-performance thermal management systems and solar-energy applications.