In the present study, a Caputo–Fabrizio (C–F) time-fractional derivative is introduced to the governing equations to present the flow of blood and the transport of magnetic nanoparticles (MNPs) through an inclined porous artery with mild stenosis. The rheology of blood is defined by the non-Newtonian visco-elastic Jeffrey fluid. The transport of MNPs is used as a drug delivery application for cardiovascular disorder therapy. The momentum and transport equations are solved analytically by using the Laplace transform and the finite Hankel transform along with their inverses, and the solutions are presented in the form of Laplace convolutions. To display the solutions graphically, the Laplace convolutions are solved using the numerical integration technique. The study presents the impacts of different governing parameters on blood and MNP velocities, volumetric flow rate, flow resistance, and skin friction. The study demonstrates that blood and MNP velocities boost with an increase in the fractional order parameter, Darcy number, and Jeffrey fluid parameter. The volumetric flow rate decreases and flow resistance increases with enhancement in stenosis height. The non-symmetric shape of stenosis and the rheology of blood decrease skin friction, whereas enhancement in MNP concentration increases skin friction. A comparison of the present result with the previous work shows excellent agreement. The present study will be beneficial for the field of medical science to further study atherosclerosis therapy and other similar disorders.

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