Alumina nanoparticles (Al₂O₃) are one of the essential metal oxides and have a wide range of applications and unique physio-chemical features. Most notably, alumina has been shown to have thermal properties such as high thermal conductivity and a convective heat transfer coefficient. Therefore, this study is conducted to integrate the adsorption of Al₂O₃ in mineral oil-based Maxwell fluid. The ambitious goal of this study is to intensify the mechanical and thermal properties of a Maxwell fluid under heat flux boundary conditions. The novelty of the research is increased by introducing fractional derivatives to the Maxwell model. There are various distinct types of fractional derivative definitions, with the Caputo fractional derivative being one of the most predominantly applied. Therefore, the fractoinal-order derivatives are evaluated using the fractional Caputo derivative, and the integer-order derivatives are evaluated using the Crank–Nicolson method. The obtained results are graphically displayed to demonstrate how all governing parameters, such as nanoparticle volume fraction, relaxation time, fractional derivative, magnetic field, thermal radiation, and viscous dissipation, have a significant impact on fluid flow and temperature distribution.