This paper examines the magneto hydrodynamic two-phase blood (Casson fluid) flow in a vessel with heat conduction
between blood and particles. The temperature of both phases is also considered. The model for the flow
under consideration is formulated in terms of partial differential equations. Then the classical model is generalized
by utilizing the Caputo fractional order derivative. The generalized equations are then non-dimensionalized
by using appropriate dimensionless variables. The exact dimensionless solutions are obtained via the joint
application of Laplace & Hankel integral transforms. The influence of various embedded parameters on both
the velocities (blood and magnetic particles) and the temperature distribution are presented graphically. It is
worth noting that the particle and blood velocities decrease for increasing the values of magnetic parameter (H)
which is useful to control the blood flow during magnetic therapy (for treating pain, such as the back, foot, or
joint pain) and surgeries. It is worth noting that fractional model better describes the flow behavior than classical
model by providing virous integral curves as shown in Fig.