Magnetic drug targeting during Caputo-Fabrizio fractionalized blood flow through a permeable vessel

Nanoparticle-based drug targeting is an important platform for the treatment of cardiovascular disorders. Magnetic drug targeting is more significant as it is a noninvasive procedure and biocompatible. The present problem aims to understand magnetic drug delivery to a specific location in a permeable blood vessel under the vibration and magnetic environment. Caputo-Fabrizio fractional-order time derivatives are used in the governing equations. The momentum equations are solved analytically and presented in the form of Lorenzo-Hartley and Robotonov-Hartley functions and convolution of the Laplace transform. Convolution integrations are solved by using the numerical integration technique. The Fourth order Runge-Kutta method (RK4) is used to solve the force balance equation. The influence of pertinent parameters such as Reynolds number, pulsatile frequency, magnetic field strength, Darcy number and fractional-order parameters are presented through graphs. It is observed that increasing Reynolds number results in decreasing the tendency of the drug to capture near the tumor site, whereas the pulsatile frequency presents an opposite phenomenon. Increasing the magnetic field strength and Darcy number boosts the capture efficiency of drug particles near the tumor site. The short memory effect efficiently captures the magnetic drug carriers to a specific location under the action of suitable magnetic field strength.