This study investigates a fractional-order time derivative model of non-Newtonian magnetic blood flow in the presence of thermal radiation and body acceleration through an inclined artery. The blood flow is formulated using the Casson fluid model under the control of a uniformly distributed magnetic field and an oscillating pressure gradient. Caputo-Fabrizio's fractional derivative mathematical model was used, along with Laplace transform and the finite Hankel transform technique. Analytical expressions were obtained for the velocity of blood flow, magnetic particle distribution, and temperature profile. These distributions are presented graphically using Mathcad software. The results show that the velocity increases with the time, Reynolds number and Casson fluid parameters, and diminishes when Hartmann number increases. Moreover, fractional parameters, radiation values, and metabolic heat source play an essential role in controlling the blood temperature. More precisely, these results are beneficial for the diagnosis and treatment of certain medical issues.