In recent decades, the study of non‐Newtonian fluids has attracted the interest of numerous researchers. Their study is encouraged by the significance of these fluids in fields including industrial implementations. Furthermore, the importance of heat and mass transfer is greatly increased by a variety of scientific and engineering processes, including air conditioning, crop damage, refrigeration, equipment power collectors, and heat exchangers. The key objective of this work is to use the mathematical representation of a chemically reactive Casson‐Maxwell fluid over a stretched sheet circumstance. Arrhenius activation energy and aspects of the magnetic field also have a role. In addition, the consequences of both viscous dissipation, Joule heating, and nonlinear thermal radiation are considered. The method transforms partial differential equations originating in fluidic systems into nonlinear differential equation systems with the proper degree of similarity which is subsequently resolved utilizing the Lobatto IIIA technique’s powerful computing capabilities. It is important to recall that the velocity profile drops as the Maxwell fluid parameter increases. Additionally, the increase in the temperature ratio parameter raises both the fluid’s temperature and the corresponding thickness of the boundary layer.

This paper estimated the problem of one-dimensional generalized thermoelastic half-space in medium considering two models: the Lord and Shulman (LS) model and the Dual-Phase-Lag (DPL) model. We assumed that the surface of the half-space was free from traction force and under an exponentially varying external heat source at the boundary with time. The technique of homotopy perturbation has been applied to find the approximate solution for the interactions of thermoelasticity with the applied boundary condition. The effect of a heat source that varies with the time and the free traction force are investigated for the temperature, displacement, and stress. The numerical results obtained are presented graphically to show the influence of the new external parameters. The results obtained illustrate the strong impacts on the displacement, temperature, and stress with the variations in the two models as well as the relaxation time parameter. The results show the agreement between the present results and the previous obtained results of the phenomenon and applicable, especially in biology, acoustics, engineering, and geophysics.

The document is presented to investigate momentum and thermal attributes of Maxwell liquid flow over a stretchable surface by inducting ferrite particles along with taking account of homogeneous-heterogeneous reactions. Two types of ferrite particles, namely, nickel zinc ferrite and magnetite ferrite , are considered and non-Newtonian fluid represented by Maxwell model is decided as base fluid blood is used. To elaborate effective use of ferrite particles, magnetization is provided by placing a single dipole. Heat transfer aspects are estimated through Cattaneo-Christov model, which includes thermal relaxation phenomena. The governing equations are changed into ODEs setup by obliging suitable variables. Subsequently, a solution is attained numerically by implementing shooting and RK methods jointly. The impact of involved pertinent parameters on associated momentum and thermal profiles is analyzed in graphical and tabular manner. It is measured that large intensity of homogeneous reaction weakens the concentration field, while ferrohydrodynamic interaction declines the flow velocity.

In this paper, we present an efficient, new, and simple programmable method for finding approximate solutions to fractional differential equations based on Bernoulli wavelet approximations. Bernoulli Wavelet functions involve advantages such as orthogonality, simplicity, and ease of usage, in addition to the fact that fractional Bernoulli wavelets have exact operational matrices that improve the accuracy of the applied approach. A fractional differential equation was simplified to a system of algebraic equations using the fractional order integration operational matrices of Bernoulli wavelets. Examples are used to demonstrate the technique’s precision.

Diabetes is a chronic disease and a major public health concern all over the world, even when made feasible to learn about the root cause of the disease by awareness along with the methods of prevention. This study introduces a mathematical deterministic model that describes the progression of type 2 diabetes, integrating a component of awareness and a saturation treatment function named Holling type II. The presented work investigates and numerically analyzes the impact of various treatment strategies, such as consistent physical activity, a healthy diet, access to medical services, and the efficacy of treatments. The research findings indicate that the use of Holling type II treatment functions can prevent minor and major complications related to diabetes.

Human papillomavirus is a sexually transmitted disease and the major cause of human cancers such as cervical, vulva, rectal, anal, and penile cancer. These cancers lead to the death of many people annually especially cervical cancer in women. This paper presents a deterministic compartmental model for the transmission of human papillomavirus and its progression to cancer. The disease-free equilibrium, reproduction number, and endemic equilibrium are determined. The disease-free equilibrium is both locally and globally asymptotically stable when the vaccination reproduction number (a control parameter) is less than one. The unique endemic equilibrium exists when the vaccination reproduction number exceeds one and the vaccine’s efficacy is negligible. However, the model undergoes a backward bifurcation when the reproduction number approaches one. The bifurcation clears when the vaccine’s efficacy is negligible. With the negligible vaccine efficacy, the endemic equilibrium is locally stable and globally stable. The model is fitted to real cervical cancer data released from Zambia that agreed with the predicted data. The fitted parameters are used for the numerical simulations. The simulation verified the global stability of the disease-free and endemic equilibrium. The numerical simulation results reveal that: different or same-sex contact leads to fewer infections than both contacts, vaccinating girls alone will slightly reduce the susceptibility of adult women but has no effect on the susceptibility of men, vaccinating only girls has an insignificant impact in reducing the number of women with cervical and other HPV-induced cancers, while vaccinating children and adults of both sex show a significant effect in reducing the cervical cancer cases.