Fractional electro-magneto transport of blood modeled with magnetic particles in cylindrical tube without singular kernel

The electro-kinetic transport of blood flow mixed with magnetic particles in the circular channel was investigated. The flow was subjected to an external electric and uniform magnetic field. The fluid was driven by pressure gradient and perpendicular magnetic field to the flow direction. Due to the usefulness and suitability of Caputo–Fabrizio fractional order derivative without singular kernel in fluid flow modeling and mass transfer phenomena, the governing equations were modeled as Caputo–Fabrizio time fractional partial differential equations and solved for \(\alpha \in \left( {0,\,1} \right]\). The analytical solutions for the velocities of blood flow and magnetic particles were obtained by using Laplace, finite Hankel transforms and Robotnov and Hartley’s functions, respectively. Mathematica software was used to simulate the influences of fractional parameter \(\alpha\), Hartmann number and Reynolds number on the velocities of blood and magnetic particles. The findings are important for controlling bio-liquids in the devices used for analysis and diagnosis in biological and medical applications.