Journal of Advanced Research in Materials Science 72, Issue 1 (2020) 15-30 15 Journal of Advanced Research in Materials Science Journal homepage: www.akademiabaru.com/arms.html ISSN: 2289-7992 The Effects of Magnetic Casson Blood Flow in an Inclined Multi-stenosed Artery by using Caputo-Fabrizio Fractional Derivatives Dzuliana Fatin Jamil 1 , Salah Uddin 1 , Rozaini Roslan 1,* 1 Department of Mathematics and Statistics, Fakulti Sains Gunaan danTeknologi, Universiti Tun Hussein Onn Malaysia, 84600 Panchor, Johor, Malaysia ARTICLE INFO ABSTRACT This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under the influence of a uniformly distributed magnetic field and an oscillating pressure gradient. The blood is modelled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo Fabrizio derivative without singular kernel. Exact analytical solutions are obtained by using the Laplace and finite Hankel transforms for both velocities. The velocities of blood flow and magnetic particles are graphically presented. It shows that the velocity increases with respect to the Reynolds number and the Casson parameter. Meanwhile, the velocity decreases as the Hartmann number increases. These results are useful for the diagnosis and treatment of certain medical problems. Keywords: Caputo Fabrizio derivative; Blood flow; Magnetohydrodynamics; Multi-stenosis Copyright © 2020 PENERBIT AKADEMIA BARU - All rights reserved 1. Introduction A detailed literature survey shows that cardiovascular disease is one of the fatal diseases currently. The main reason is due to the unusual hemodynamics within the bloodstream. Hemodynamic is the knowledge of blood circulation, which is useful in the diagnosis of coronary illness. The reason behind the malfunction of cardiovascular system is the presence of fats, cholesterol and lipoproteins at the sites of atherosclerotic lesion in the artery [1]. In recent years, due to its great importance in the human cardiovascular system, the study of blood flow through constricted arteries has received a great deal of attention [2-4]. Blood vessels have been regarded as having zero inclination, which were treated as horizontal in most available studies. Physically, these arteries are tilted [5]. Prasad and Radhakrishnamacharya [6] considered the steady blood flow through an inclined non-uniform tube with multiple stenoses. Agarwal and Varshney [7] studied the flow of Herschel-Bulkley fluid through an inclined tube of non-uniform cross-section with multiple stenoses. Biswas and Paul [8] observed the steady blood flow through an inclined tapered vessel, where the blood was modelled as Newtonian fluid and the slip vessel wall condition was applied. * Corresponding author. E-mail address: rozaini@uthm.edu.my https://doi.org/10.37934/arms.72.1.1530 Open Access