This study presents a theoretical investigation of the time-dependent electro-osmotic hemodynamics of a fractional second-grade fluid laden with tetra-hybrid nanoparticles (Au, Al₂O₃, TiO₂, and SWCNTs) flowing through a compliant bifurcated artery affected by multiple atherosclerotic stenoses. The mathematical model incorporates the coupled effects of time-varying electro-osmotic forcing, arterial wall elasticity, and complex multi-stenosed bifurcation geometry to realistically capture the dynamics of blood-based nanofluid transport and targeted drug delivery. A fractional constitutive framework is employed to account for the hereditary and memory-dependent viscoelastic behavior of blood, while the inclusion of tetra-hybrid nanoparticles significantly enhances the effective thermal and electrical conductivities, thereby improving flow regulation and nanoparticle dispersion. The resulting nonlinear fractional governing equations are solved numerically using Mathematica software. The parametric analysis demonstrates that an intensification of the time-dependent electro-osmotic field markedly suppresses axial velocity in both the parent and daughter arteries, while an increase in the fractional-order parameter further attenuates the velocity due to enhanced memory effects. The temperature field is observed to decrease with increasing nanoparticle volume fraction, whereas the absence of a nanolayer around nanoparticles leads to a pronounced enhancement in temperature, accompanied by dominant velocity modulation. The present model elucidates the synergistic interplay between electro-osmotic actuation, wall compliance, and fractional rheology in optimizing nanofluid-based drug transport, offering novel insights for the design of advanced electrohydrodynamic therapeutic strategies in cardiovascular disease management.