<p>This study investigates the effects of thermal radiation and thermal diffusion on unsteady, viscous, incompressible, electrically conducting MHD heat and mass transfer in Cu and TiO₂ nanofluid flow past an oscillating semi-infinite vertical moving porous plate. The analysis considers Joule heating, viscous dissipation, and an applied transverse magnetic field. Initially, it is assumed that both the plate and the surrounding fluid are at the same temperature and concentration throughout the flow region. Subsequently, the plate is given a constant temperature, with buoyancy effects driving the fluid in the upward direction, while gravity acts as the opposing force. The performance of Cu and TiO₂ in water is of particular interest. The governing flow equations, which are partial differential equations with initial and boundary conditions, are derived. By introducing suitable nondimensional quantities, the nonlinear partial differential equations are transformed into dimensionless form and solved analytically using the perturbation method. Expressions for skin friction, the rate of heat transfer, and the rate of mass transfer are also derived and presented in tabular form. The study analyzes the characteristics of flow, heat, and mass transfer in Cu–TiO₂ nanofluids, focusing on key influencing factors. The results indicate that the velocity increases with rising buoyant forces and Soret factors, especially in the liquid region. The thermal and solutal buoyant effects influence momentum, continuously growing until reaching a peak. Additionally, the concentration decreases as the chemical response factor increases throughout the fluid region.</p>