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Hydrodynamic flow of Newtonian blood mixed with magnetic particles (red blood cells) through stenosed region is studied in this paper. The fluid is acted upon by an oscillating pressure gradient in a perpendicular magnetic field. Governing fractional momentum equations are analytically solved for axial velocities. Graphical analysis of velocity profiles against various physiological parameters is developed by coding in Mathematica. Effect of Caputo fractional operator a on axial velocities is also considered. Results show that blood and magnetic particles has increasing effect with maximum height of the stenosis and electric field, whereas, it has a decreasing effect with perpendicular magnetic field. Hence, the flow of blood can be controlled by applying sufficient and strong electric and magnetic field. This is an important fact in medical diagnosis and clinical treatment of various cardiovascular diseases, hypertension and atherosclerosis.