Hybrid nanofluids have gained too much attention due to their enhanced thermophysical properties and practical applications. In comparison to conventional nanofluids, their capacity to enhance heat transport is impressive. The simultaneous numerical calculations of hybrid and mono nanofluids across an exponentially shrinking surface in a porous medium are taken into consideration here. The analysis of the thermal energy distribution is carried out by using the convective boundary conditions. Shrinking, permeability, and magnetohydrodynamic controlled the motion of the flow. The objective of this research is to conduct stability analysis and identify the existence of dual solutions in the presence of heat source/sink and nonlinear Roseland thermal radiation. The technique, bvp4c, a collocation method is used to achieve numerical results. It is noted that the energy transport is enhanced immensely due to the presence of a mixture of nanoparticles (hybrid) in comparison to mono nanofluids. The stability analysis shows that the solutions for the upper branch were stable, while the solutions for the lower branch were unstable. Moreover, shrinking parameter contributes significantly to exhibit the dual nature of the solutions. Due to the increment in the heat generation/absorption and temperature ratio, the kinetic energy is inclined, which causes the temperature distribution to rise for both branches. For stable branches, an increase in wall stress values is evident as a result of permeability and stretching of sheet, whereas unstable branches show the opposite trend.