Nanofluids can be used in different solar thermal systems. Solar energy devices utilized in industries and nanofluids as a source of solar energy in thermal engineering are two other sources of solar energy, according to the article. This work inspects a viscous, incompressible nanofluid made of different (graphene oxide (GO) and molybdenum disulfide (MoS2)) nanoparticles suspended in carboxymethyl cellulose (CMC). The governed model also considers permeability and angled magnetic effects. Due to memory effects, classical derivatives cannot explore and estimate the physical significance of several fluid limitations. We have addressed the issues with nanofluid suspension using the Prabhakar fractional derivative definition, the quickest and latest modern fractional technique. First, the governed leading equations are transferred to a fractional version using the integral transform technique and Laplace transform, and then it is resolved with various numerical approaches. Each constraint visual impact and significance are analyzed by varying their considered values. The numerical influences of the heat and flow rate are observed at multiple time values. Therefore, we deduce that the momentum and heat profiles are slowed as the Prabhakar fractional restraints increase. While with the increment in the radiation parameter, the velocity profile shows an increasing behavior. Furthermore, the impact of graphene oxide-based suspension is more significant than molybdenum disulfide nanofluid on all governed equations due to the physical features of the considered nanoparticles.