This study examines a viscous, incompressible, free-convective Casson fluid flow over an inclined plate, which characterizes an asymmetrical nanofluid flow and heat transfer behavior. Here, the two different nanofluids are basically made of molybdenum disulfide (MoS2) with CMC-based fluid and graphene oxide (GO) nanoparticles with CMC-based fluid to form a particular (CMC/MoS2) nanofluid and (CMC/GO) nanofluid. The Newtonian heating effect, slip boundary, porosity, and inclined magnetic effects are also considered. When memory effects are present, conventional PDEs are unable to investigate and evaluate the physical behavior of various flow parameters. We employed the Prabhakar fractional derivative, the best and most current fractional mathematical operator, to tackle the considered nanofluid problem. Using the integral transform approach, Laplace transforms, the non-dimensional governed model is converted into a fractional model and solved. The graphical analysis examines the influence and symmetrical behavior of significant physical and fractional parameters. The numerical effects of the Nusselt number, Sherwood number, and skin friction are also looked at, at various sundry values of the time. As a result, we conclude that increasing Prabhakar fractional constraints causes the thermal and momentum profiles to decelerate down. In addition, for two distinct values of time, 0.8 and 1.8, improvements of 3.823% and 5.042%, respectively, are observed in the mass transfer rate for the higher impacts of the Prabhakar fractional parameter, α, while the heat transfer rate declines by 10.065% and 15.908%, respectively. Also, the shear stress upsurges by 0.881% and 2.482%, respectively, for the change values of time 0.8 and 1.8 with higher values of Prabhakar fractional parameter α. Furthermore, with varying time, the accompanying criteria are satisfied, and the velocity and temperature fields both expand asymptotically in the y-direction and decline away from the plate. When comparing the two nanofluids, the (CMC/MoS2) nanofluid has a somewhat higher thermal and flow rate than the (CMC/GO) nanofluid. The studies indicated that increasing the volume percentage of nanoparticles causes heat transmission to be enriched.