Showing papers in "Mathematical Methods in The Applied Sciences in 2020"

The analysis of a time delay fractional COVID-19 model via Caputo type fractional derivative.

Abstract: Novel coronavirus (COVID-19), a global threat whose source is not correctly yet known, was firstly recognised in the city of Wuhan, China, in December 2019. Now, this disease has been spread out to many countries in all over the world. In this paper, we solved a time delay fractional COVID-19 SEIR epidemic model via Caputo fractional derivatives using a predictor-corrector method. We provided numerical simulations to show the nature of the diseases for different classes. We derived existence of unique global solutions to the given time delay fractional differential equations (DFDEs) under a mild Lipschitz condition using properties of a weighted norm, Mittag-Leffler functions and the Banach fixed point theorem. For the graphical simulations, we used real numerical data based on a case study of Wuhan, China, to show the nature of the projected model with respect to time variable. We performed various plots for different values of time delay and fractional order. We observed that the proposed scheme is highly emphatic and easy to implementation for the system of DFDEs.

Hybrid ferrofluid along with MWCNT for augmentation of thermal behavior of fluid during natural convection in a cavity

Abstract: Current pagination concerns with exploration regarding thermal characteristics induced by Hybridization of with MWCNT in a permeable tank filled with viscous fluid with magnetization. Roseland approximation is obliged to configure radiative heat flux aspects. Modeling and structuring of considered problem is established in partial differential setup. CVFEM is implemented to seek out solution of constructed differential layout. Data establishing properties of with MWCNT’s is disclosed in tabular format. Impression of sundry variables in view of isotherm and stream pattern is divulged. Local convective thermal rate against involved variables in 3D snapshots is captured. Test about grid independence and comparison with conducted work to get assurance of present finding is explicated. It is deduced that heat transfer along walls enhances verses Rayleigh and Darcy parameters whereas delineates against mounting effect of magnetic field strength.

Fangzhu (方诸): An ancient Chinese nanotechnology for water collection from air: History, mathematical insight, promises, and challenges

Abstract: Fangzhu, which has been lost for thousands of years, is an ancient device for water collection from air, its mechanism is unknown yet. Here we elucidate its possible surface-geometric and related physical properties by the oldest the Yin-Yang contradiction. In view of modern nanotechnology, we reveal that Fangzhu’s water-harvesting ability is obtained through a hydrophilic-hydrophobic hierarchy of the surface, mimicking spider web’s water collection, lotus or desert beetle’s water intake. The convex-concave hierarchy of Fangzhu’s textured surface enables it to have low wettability(high geometric potential) to attract water molecules from air through the nano-scale convex surface and transfer the attracted water along the concave surface to the collector. A mathematical model is established to reveal three main factors affecting its effectiveness, i.e., the air velocity, the surface temperature and surface structure. The lost technology can play an extremely important role in modern architecture, ocean engineering, transportation and others to catch water from air for everyday use.

Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation

Abstract: This paper presents analytical-approximate solutions of the time-fractional Cahn-Hilliard (TFCH) equations of fourth and sixth-order using the new iterative method (NIM) and q-homotopy analysis method (q-HAM). We obtained convergent series solutions using these iterative methods. The simplicity and accuracy of these methods in solving strongly nonlinear fractional differential equations is displayed through the examples provided. In the case where exact solution exists, error estimates are also investigated.