METHODS: The Casson fluid was used to model the blood that flows under the influences of uniformly distributed magnetic field and oscillating pressure gradient. The governing fractional differential equations were expressed using the Caputo Fabrizio fractional derivative without singular kernel.
RESULTS: The analytical solutions of velocities for non-Newtonian model were then calculated by means of Laplace and finite Hankel transforms. These velocities were then presented graphically. The result shows that the velocity increases with respect to Reynolds number and Casson parameter, while decreases when Hartmann number increases.
CONCLUSIONS: Casson blood was treated as the non-Newtonian fluid. The MHD blood flow was accelerated by pressure gradient. These findings are beneficial for studying atherosclerosis therapy, the diagnosis and therapeutic treatment of some medical problems.