Given the importance and use of electrically conducted nanofluids, this work aims to examine an engine-oil-based nanofluid including various nanoparticles. In the current study, a fractional model for inspecting the thermal aspect of a Brinkman-type nanofluid, composed of (molybdenum disulfide (MOS2) and graphene oxide (GO) nanoparticles flows on an oscillating infinite inclined plate, which characterizes an asymmetrical fluid flow, heat, and mass transfer. Furthermore, the Newtonian heating effect, magnetic field, and slip boundary conditions were taken into account. The objectives for implementing the Prabhakar-like fractional model are justified because this fractional algorithm has contemporary definitions with no singularity restrictions. Furthermore, the guided fractional model was solved using the Laplace transform and several inverse methods. The obtained symmetrical solutions have been visually analyzed to investigate the physics of several relevant flow parameters on the governed equations. Some exceptional cases for the momentum field are compiled to see the physical analysis of the flowing fluid symmetry. The results show that the thermal enhancement can be progressively improved with the interaction of the molybdenum disulfide-engine oil-based nanofluid suspension, rather than with the graphene oxide mixed nanoparticle fluid. Furthermore, the temperature and momentum profiles enhance due to the factional parameters for molybdenum disulfide and the graphene oxide-engine oil-based nanofluid suspension. This study’s graphical and numerical comparison with the existing literature has shown a very close resemblance with the present work, which provides confidence that the unavailable results are accurate. The results show that an increase improved the heat transmission in the solid nanoparticle volume fractions. In addition, the increment in the mass and heat transfer was analyzed in the numerical evaluation, while the shear stress was enhanced with the enhancement in the Prabhakar fractional parameter α.