Fractional Order Analysis of Pulsatile Blood-Nanoparticle Flow in Femoral and Coronary Arteries Under Magnetic and Thermal Influences

The utilization of magnetic particles in biomedicine and clinical therapies has garnered significant interest in recent years. The distinctive characteristics of magnetic particles have facilitated their application in various medical techniques. These techniques enable for the targeted delivery of medication within cells as well as providing simple diagnostic tools. Recent advancements have enhanced MRI, drug delivery to infected tissues, and hyperthermia through the use of magnetic particles. This research presents a mathematical study for two-phase unsteady pulsatile blood flow through femoral and coronary arteries in the presence of suspended nanoparticles, body acceleration, temperature variations and an external magnetic field. Related problem is simulated by using Caputo fractional derivative operator and is solved by applying integral transforms. Closed form expressions for the velocity of blood and nanoparticles are obtained and expressed in the form of Lorenzo-Hartley generalized functions. In addition, to comprehend the influence of fractional order parameter and material factors including amplitude, lead angle, frequency of body acceleration, magnetic field, particle concentration and temperature effects a thorough graphical analysis is done and concluded with noteworthy results.