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The recent progress in nanotechnology developed more stable nanofluid models with ultra-high thermal performances. The immersion of hybrid nanoparticles in the base fluid presents novel applications in the thermal transport processes, solar energy, engineering devices, and heating systems. This continuation identified the thermal outcomes of the hybrid nanofluid model with the water base fluid. The thermal investigation is encountered by utilizing the copper oxide (CuO), silver (Ag), and titanium dioxide (TiO2) nanoparticles. The thermal selection of these three types of nanoparticles is associated with impressive characteristics and stability. To attain the more progressive thermal aspects, thermal radiation consequences are also focused. The inclined infinite configuration is assumed where these nanoparticles and base fluid are specified. The comparative results for the hybrid nanofluid and modified hybrid models are pronounced. The fractional model of dimensionless partial differential leading equations is formulated by following the recent definitions of fractional derivatives, namely, Atangana–Baleanu and Caputo–Fabrizio fractional derivatives. The semi-analytical simulations are performed via the Laplace technique for nanoparticles temperature and velocity inspection. The significances of the fractional parameter and volume fraction are observed for the velocity profile. [ABSTRACT FROM AUTHOR]