In this investigation, the nonplanar (spherical and cylindrical) modified fifth-order Korteweg–de Vries (nmKdV5) equation, otherwise known as the nonplanar modified Kawahara equation (nmKE), is solved using the ansatz approach. Two general formulas for the semi-analytical symmetric approximations are derived using the recommended methodology. Using the obtained approximations, the nonplanar modified Kawahara (mK) symmetric solitary waves (SWs) and cnoidal waves (CWs) are obtained. The fluid equations for the electronegative plasmas are reduced to the nmKE as a practical application for the obtained solutions. Using the obtained solutions, the characteristic features of both the cylindrical and spherical mK-SWs and -CWs are studied. All obtained solutions are compared with each other, and the maximum residual errors for these approximations are estimated. Numerous researchers that are interested in studying the complicated nonlinear phenomena in plasma physics can use the obtained approximations to interpret their experimental and observational findings.

With the increasing need for effective elderly care solutions, this paper presents a novel federated learning-based system that uses smartphones as edge devices to monitor and enhance elderly care in real-time. In this system, elderly individuals carry smartphones equipped with Inertial Measurement Unit (IMU) sensors, including an accelerometer for activity recognition, a barometer for altitude detection, and a combination of the accelerometer, gyrometer, and magnetometer for location tracking. The smartphones continuously collect real-time data as the elderly individuals go about their daily routines. These data are processed locally on each device to train personalized models for activity recognition and contextual monitoring. The locally trained models are then sent to a federated server, where the FedAvg algorithm is used to aggregate model parameters, creating an improved global model. This aggregated model is subsequently distributed back to the smartphones, enhancing their activity recognition capabilities. In addition to model updates, information on the users’ location, altitude, and context is sent to the server to enable the continuous monitoring and tracking of the elderly. By integrating activity recognition with location and altitude data, the system provides a comprehensive framework for tracking and supporting the well-being of elderly individuals across diverse environments. This approach offers a scalable and efficient solution for elderly care, contributing to enhanced safety and overall quality of life.

The boundary layer micropolar fluid over a horizontal plate embedded in a non-Darcy porous medium is investigated in this study. This paper is solely focused on contributions oriented towards the application of micropolar fluid flow over a stretching sheet. The prime equations are renewed to ordinary differential equations with the assistance of similarity transformation; they are then subsequently solved numerically using the spectral quasi-linearization method (SQLM) for direct Taylor series expansions that can be applied to non-linear terms in order to linearize them. The spectral collocation approach is then applied to solve the resulting linearized system of equations. The paper acquires realistic numerical explanations for rapidly convergent solutions using the spectral quasi-linearization method. Convergence of the numerical solutions was monitored using the residual error of the PDEs. The validity of our model is established using error analysis. The impact of different geometric parameters on angular velocity, temperature, and entropy generation numbers are presented in graphs. The results show that the entropy generation number decelerates with an increase in Reynolds number and Brinkmann number. The velocity profile increases with the increasing material parameter. The results indicate that the fluid angular velocity decreases throughout the boundary layer for increasing values of the material parameter.

Kinetic Alfvén waves (KAWs) are investigated in an Oxygen–Hydrogen plasma with electrons following the behavior of $rq$-distribution in an upper ionosphere. We aim to study low-frequency and long wavelengths at 1700 kms in the upper ionosphere of Earth as detected by Freja satellite. The fluid model and reductive perturbation method are combined to obtain the evolutionary wave equations that can be used to describe both fractional and non-fractional KAWs in an Oxygen–Hydrogen ion plasma. This procedure is used to obtain the integer-order Korteweg–de Vries (KdV) equation and then analyze its solitary wave solution. In addition, this study is carried out to evaluate the fractional KdV (FKdV) equation using a new approach called the “Tantawy technique” in order to generate more stable and highly accurate approximations that will be utilized to accurately depict physical events. This investigation also helps locate the existence regions of the solitary waves (SWs), and in turn displays that the characteristics of KAWs are affected by a number of physical factors, such as the nonthermal parameters/spectral indices “r”, “q”, and obliqueness (characterized by $l_z$). Depending on the parameter governing the distribution, especially the nonthermality of inertialess electrons, the $rq$-distribution of electrons has a major impact on the properties of KAWs.

This paper introduces fractional-order into a mathematical model of HIV infection of CD4$ ^{+} $ T-cells combining with the rate of multiply uninfected CD4$ ^{+} $ T-cells through mitosis and stem cell therapy. The paper shows the theoretical studies including positivity and stability of the solution. In addition, the numerical solutions are obtained and illustrated. The results show that the stem cell's therapy increases the quality of a HIV patient's life only for short time. This results are consistent with medical case studies.