Innovative Approximate Solution for Jerk Model of Non-Newtonian Bio-Nanofluid in Fractal Space via Highly Efficient Linear Approximation

In this article, we present a new approximate solution for blood nanofluid having gold nanoparticles as it flows near a stretching porous cylinder in fractal space. A Casson non-Newtonian magneto-bio-nanofluid flowing through a porous medium is considered a potential application in chemotherapy for eradicating cancer cells. Without the need for the nonperturbative approach, the proposed solution uses an alternative approach to dealing with nonlinear problems. This approach transforms the nonlinear cubic jerk model resulting from the simplification of the governing fractional partial differential equations into an equivalent linear formula. This approach is known as highly efficient linear approximation (HELA) or non-perturbation technique (NPT), and this represents a significant advancement over traditional perturbation methods in the analysis of non-linear systems. As a robust mathematical approach, it excels at handling a wide range of coefficient values, particularly in cases of clear nonlinearity. This study also utilized the masking technique simultaneously with HELA, which played a crucial role, as they simplify the complex dynamics of the system, making it more amenable to analysis. The numerical solution by the Runge–Kutta fourth-order (RK-4) method integrated with a shooting technique compared favorably with graphs drawn for the analytical solution from the proposed strategy HELA. The current results show that an increase in the fractal factors enhances the resistance to fluid motion, leading to a suppression of the velocity field. Physically, this often relates to the complexity of the medium or the fractal nature of the transport process, where higher fractal dimensions or factors can lead to slower diffusion or flow rates, like the role of porous media. Therefore, the current study has significant implications in the promotion of nanotechnology fields in medicine, particularly the use of gold nanoparticles in chemotherapy for the eradication of cancerous cells.