Faculty of Science, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand.
Department of Mathematics, City University of Science and Information Technology, Peshawar, 25000, Pakistan.
Sci Rep. 2021 Oct 14;11(1):20429. doi: 10.1038/s41598-021-00004-3.
Fractional calculus characterizes a function at those points, where classical calculus failed. In the current study, we explored the fractional behavior of the stagnation point flow of hybrid nano liquid consisting of TiO and Ag nanoparticles across a stretching sheet. Silver Ag and Titanium dioxide TiO nanocomposites are one of the most significant and fascinating nanocomposites perform an important role in nanobiotechnology, especially in nanomedicine and for cancer cell therapy since these metal nanoparticles are thought to improve photocatalytic operation. The fluid movement over a stretching layer is subjected to electric and magnetic fields. The problem has been formulated in the form of the system of PDEs, which are reduced to the system of fractional-order ODEs by implementing the fractional similarity framework. The obtained fractional order differential equations are further solved via fractional code FDE-12 based on Caputo derivative. It has been perceived that the drifting velocity generated by the electric field E significantly improves the velocity and heat transition rate of blood. The fractional model is more generalized and applicable than the classical one.
分数微积分在经典微积分失效的点上对函数进行描述。在本研究中，我们探索了由 TiO 和 Ag 纳米粒子组成的混合纳米液体在拉伸薄板上的驻点流动的分数行为。银 Ag 和二氧化钛 TiO 纳米复合材料是最重要和最引人注目的纳米复合材料之一，在纳米生物技术中发挥着重要作用，特别是在纳米医学和癌症细胞治疗中，因为这些金属纳米粒子被认为可以提高光催化作用。在拉伸层上的流体运动受到电场和磁场的影响。通过实施分数相似性框架，将问题表述为 PDE 系统，并将其简化为分数阶 ODE 系统。通过基于 Caputo 导数的分数代码 FDE-12 进一步求解得到的分数阶微分方程。已经发现，电场 E 产生的漂移速度显著提高了血液的速度和热传递速率。分数模型比经典模型更具普遍性和适用性。
