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This paper addresses a mixed and free convective Casson nanofluid flowing on an oscillating inclined poured plate with sinusoidal heat transfers and slip boundaries. As base fluid water is supposed and the suspension of nanofluid is formulated with the combination of individual copper $ \left(Cu\right) $, titanium dioxide $ \left(Ti{O}_{2}\right) $ and aluminum oxide $ \left(A{l}_{2}{O}_{3}\right) $ as nanoparticles, the dimensionless governing equations are generalized based on Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) fractional operators for developing a fractional form. Then, for the semi-analytical solution of the momentum and thermal profiles, the Laplace transformation is utilized. To discuss the influences of various pertinent parameters on governing equations, graphical tablecomparison of the Nusselt number and skin friction is also inspected at different times and numerical schemes. As a result, it has been concluded that both the momentum and energy profiles represent the more significant results for the AB-fractional model as related to the CF-fractional model solution. Furthermore, water-based titanium dioxide $ \left(Ti{O}_{2}\right) $ has a more progressive impact on the momentum as well as the thermal fields as compared to copper $ \left(Cu\right) $ and aluminum oxide $ \left(A{l}_{2}{O}_{3}\right) $ nanoparticles. The Casson fluid parameter represents the dual behavior for the momentum profile, initially momentum field decreases due to the Casson parameter but it then reverses its impact and the fluid flow moves more progressively.