This article concerns the analysis of an unsteady stagnation point flow of Eyring-Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme.A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme (RK-4) is available to show the credibility of the Galerkin method. The numerical exploration is carried out for various governing parameters, namely, Brownian motion, steadiness,thermophoresis, stretching ratio, velocity slip, concentration slip, thermal slip, and fluid parameters, and Hartmann, Prandtl and Schmidt numbers. The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing, but the behavior is reversed for assisting cases. The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases (assisting and opposing). The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter. All the outcomes and the behavior of emerging parameters are illustrated graphically. The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method. It is concluded that said method could be extended to other problems of a complex nature.