Abstract
The aim of the article is two-fold. We first analyze and investigate free convective, unsteady, MHD blood flow with single- and multiwalled carbon nanotubes (S & MWCNTs) as nanoparticles. The blood flow has been taken across an upright vertical plate, oscillating in its own plane, and engrafted in a porous medium with slip, radiation, and porosity effects. Nanofluids consist of human blood as the base fluid and SWCNTs and MWCNTs as nanoparticles. The second aim is to discuss the three different definitions of fractional derivatives, namely, Caputo (C), Caputo-Fabrizio (CF), and Atangana-Baleanu (ABC), to obtain the solutions of such proposed models by the Adomian decomposition method. The impact of fractional and physical parameters on the concentration, velocity, and temperature of human blood in the presence of the slip effect is studied and projected diagrammatically. The article ends by providing numerical results such as the reliableness, efficiency, and significant features that are simple in computation with eminent accuracy of the process for non-Newtonian Casson nanofluid fractional order models. It is observed that the velocity of the fluid decreases with SWCNTs' and MWCNTs' volume fraction, and an increase in the CNTs' volume fraction increases blood temperature, which ultimately enhances heat transfer rates. The results acquired are in excellent correspondence with the reported results.