A number of thermal devices might benefit from the usage of nanofluids in solar power. In this research, the idea of MHD mixed convective hybrid nanofluids including grapheme oxide (GO) and molybdenum disulfide (MoS2) nanoparticles with water (H2O) and Carboxymethyl Cellulose (CMC) as base fluids in a perpendicular channel to analyze the heat transfer of the flowing fluid with the help of recent definition of fractional derivatives namely Fractal fractional derivative. The problem is expressed as PDEs with beginning and boundary conditions, and it is analyzed analytically using the Laplace transform method. The velocity, temperature, and concentration measurements are also shown in series for their appropriate Laplace inverse. Delays in parameters like nanoparticle volume sharing rate have a significant influence on these techniques. Skin friction, Nusselt, and Sherwood numbers are computed for the longitudinal channel's left and right walls, and the necessary numerical results are presented in tabular format. As a result, it is discovered that the rate of heat transfer reduces as the volume percentage of nanoparticles and the Fractal time fractional value rise. Furthermore, when comparing nanofluids, water-based (H2O + GO + MoS2) hybrid nanofluids have a greater influence on governed model than (CMC + GO + MoS2)-based hybrid nanofluids.