In this study, we have addressed the flow of hybrid nanofluid (Cu�Al2O3-Sodium Alginate), nanofluid (Cu-Sodium Alginate), and nanofluid (Al2O3-Sodium Alginate). Flow is because of the heated boundary of the channel and its different movements. The flow is modelled using Casson fluid's momentum equation, and the heat equation is generalized using the generalized Fourier's law based on Caputo-time fractional derivatives. The non-dimensional fractional partial differential equations are solved using the Laplace and Fourier transforms. The velocity and temperature show variations for different values of the fractional parameter; also, the plots are drawn for the classical model. The temperature distribution increases for the volume fractions of the nanoparticles and has maximum vales for hybrid nanoparticles with the highest chosen volume fractions values. Furthermore, intensification in heat transfer rate is increased due to hybrid nanoparticles. © 2021