This paper explores the impact of temperature on the fractionalization of magnetic nanoparticles in blood, coupled with vibratory motion influenced by rotation. The distribution systems exhibit heightened diffusivity, explored numerically through the finite difference method and the algorithm. The temperature distribution robustly responds to elevated fractional parameters, indicating a critical threshold. The study achieves a comprehensive understanding of temperature and velocity evolution in different tube zones. In comparison, single‐walled carbon nanotubes surpass multiple‐walled carbon nanotubes in distributions, while CuO nanoparticles demonstrate larger distributions at an average fractional‐order parameter of . In the observed growth region at and exhibit noteworthy temperature distributions, highlighting the fractional derivative's impact in highly diffusive models with nanoparticles. It is also noted that in this region, the temperature distribution tends to decrease for all the parameters and values examined, particularly at a low Reynolds number (). However, the introduction of nanoparticles accelerates the processes and distributions across the various observed zones. Furthermore, the accelerated behavior of each nanoparticle can be moderated based on its sphericity. By encompassing all facets of fractional order for controlled rotations, the study sheds light on the role of magnetized nanoparticles in blood dynamics, emphasizing the significance of a critical zone where certain physicochemical properties are disrupted, potentially leading to cellular disorders, and the fluidodynamic effects of vortex flow. This perspective is pivotal for addressing tissue lesions induced by vibrations, as seen in the case of coagulations, and for targeting carcinogenic areas using nanoelements.
