A fractional blood flow model, in the presence of magnetic nanoparticles, is considered in this work. The effects of activation energy and thermal radiation on the blood flowing in the oscillating elastic tube are studied. The nanofluid inside the tube is activated by the rotating effect of the charged particles, a constant external magnetic field, and the activation energy. The blood is assumed to be at a temperature and a concentration that vary with the speed of the particles. The study takes advantage of a model, which includes a fractional-order derivative of Caputo's type. The shape of nanoparticles and the speed of blood and the distributions of temperature and concentration are assimilated to Brownian motion and thermophoresis. They are calculated numerically using the L1-algorithm method. The results show that the applied magnetic field and the effects of the fractional-order parameter reduce the velocity of the nanofluid and nanoparticles, which considerably affects the temperature and concentration of the fluid. It is also found that the particle shape and fractional derivative parameters significantly influence velocities and heat transfer.