This paper introduces the effect of heat absorption (generation) and suction (injection) on magnetohydrodynamic (MHD) boundary-layer flow of Casson nanofluid (CNF) via a non-linear stretching surface with the viscous dissipation in two dimensions. By utilizing the similarity transformations, the leading PDEs are transformed into a set of ODEs with adequate boundary conditions and then resolved numerically by (4-5) th -order Runge-Kutta Fehlberg procedure based on the shooting technique. Numerical computations are carried out by Maple 15 software. With the support of graphs, the impact of dimensionless control parameters on the nanoparticle concentration profiles, the temperature, and the flow velocity are studied. Other parameters of interest, such as the skin friction coefficient, heat, and mass transport at the diverse situation and dependency of various parameters are inspected through tables and graphs. Additionally, it is verified that the numerical computations with the reported earlier studies are in an excellent approval. It is found that the heat and mass transmit rates are enhanced with the increasing values of the power-index and the suction (blowing) parameter, whilst are reduced with the boosting Casson and the heat absorption (generation) parameters. Also, the drag force coefficient is an increasing function of the powerindex and a reduction function of Casson parameter.
The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology. One aim of these models is to understand the dynamics of behavior in infectious diseases. For the new strain of coronavirus (COVID-19), there is no vaccine to protect people and to prevent its spread so far. Instead, control strategies associated with health care, such as social distancing, quarantine, travel restrictions, can be adopted to control the pandemic of COVID-19. This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods: the homotopy perturbation method (HPM) and the modi ed reduced differential transform method (MRDTM). We invoke a novel signal ow graph that is used to describe the COVID-19 model. Through our mathematical studies, it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus. The numerical simulation results are in reasonable agreement with the study predictions. The free equilibrium and stability point for the COVID-19 model are investigated. Also, the existence of a uniformly stable solution is proved.
The purpose of this article is to explore the asymptotic properties for a class of fourth-order neutral differential equations. Based on a comparison with the differential inequality of the first-order, we have provided new oscillation conditions for the solutions of fourth-order neutral differential equations. The obtained results can be used to develop and provide theoretical support for and to further develop the study of oscillation for a class of fourth-order neutral differential equations. Finally, we provide an illustrated example to demonstrate the effectiveness of our new criteria.
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