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The MHD flow of a blood-based hybrid nanofluid with thermal radiation and stenosis effects is explored in this study. Gold (Au) and Copper (Cu) hybrid nanoparticles are assumed to be distributed in the blood. Relevant governing equations are established and appropriately normalized. The Caputo fractional-order derivative is used to convert the transient terms of normalized equations into time-fractional forms, which are then semi-analytically solved using the Laplace transform method to yield complex forms of modified Bessel functions. The concentrated matrix exponential (CME) approach is used to numerically determine approximate inverse Laplace transforms of the updated equations. The distribution patterns of velocity, temperature, and concentration are evaluated graphically. The results showed that the fractional-order derivative and the height of stenosis greatly influence the velocity, temperature and concentration profiles. We also observed that both velocity and temperature decreased with increasing values of Ha. Temperature rises with increasing values of the thermal radiation parameter (Ra) and the Eckert number (Ec) whilst concentration is enhanced with rising values of the chemical reaction parameter (Cr) and the Schmidt number (Sc). Our numerical results show that relevant parameters have considerable influences on skin friction, Nusselt number, and Sherwood number, which are important for understanding blood mobility, heat and mass transfer dynamics, and treating cardiovascular illnesses. Our results are also essential for controlling blood flow, temperature and delivery of drugs to diseased arteries in the human body.