This article explores an incompressible hybrid nanofluid flow over an infinite impermeable rotating disk. The influence of a magnetic field has been added to better examine the fine point of nanoliquid flow. The main purpose of this work is to enhance our understanding of the exhaustion of energy in industrial and engineering fields. This study is mainly concerned with the von Kármán traditional flow of a rotating disk, involving carbon nanotubes (CNTs) and magnetic ferrite nanoparticles together with a carrier fluid such as water. The nonlinear system of differential equations is transformed to the dimensionless ordinary differential equation by using an appropriate similarity framework, which is further treated with the “homotopy analysis method” for the analytic solution. A mathematical calculation is provided to prove and illustrate why the hybrid nanofluids are advantageous as far as the heat transfer enhancement is concerned. Although the physical features highly rely on CNTs and iron oxide nanoparticles, it is concluded that the heat and mass transfer rate is greatly enhanced by the addition of CNTs and Fe₃O₄ nanofluids. By increasing the velocity of disk rotation, fluid temperature and velocity are significantly increased. The use of CNT + Fe₃O₄/H₂O influences the performance of thermophysical characteristics of carrier fluids more compared to magnetic ferrite nanomaterials.

Information exchange has become increasingly faster and efficient through the use of recent technological advances, such as instant messaging and social media platforms. Consequently, access to information has become easier. However, new types of cybersecurity threats that typically result in data loss and information misuse have emerged simultaneously. Therefore, maintaining data privacy in complex systems is important and necessary, particularly in organizations where the vast majority of individuals interacting with these systems is students. In most cases, students engage in data breaches and digital misconduct due to the lack of knowledge and awareness of cybersecurity and the consequences of cybercrime. The aim of this study was to investigate and evaluate the level of cybersecurity awareness and user compliance among undergraduate students at Majmaah University using a scientific questionnaire based on several safety factors for the use of the Internet. We quantitatively evaluated the knowledge of cybercrime and protection among students to show the need for user education, training, and awareness. In this study, we used a quantitative research methodology and conducted different statistical tests, such as ANOVA, Kaiser–Meyer–Olkin (KMO), and Bartlett’s tests, to evaluate and analyze the hypotheses. Safety concerns for electronic emails, computer viruses, phishing, forged ads, popup windows, and supplementary outbreaks on the Internet were well-examined in this study. Finally, we present recommendations based on the collected data to deal with this common problem.

This manuscript deals with fractional differential equations including Caputo–Fabrizio differential operator. The conditions for existence and uniqueness of solutions of fractional initial value problems is established using fixed point theorem and contraction principle, respectively. As an application, the iterative Laplace transform method (ILTM) is used to get an approximate solutions for nonlinear fractional reaction–diffusion equations, namely the Fitzhugh–Nagumo equation and the Fisher equation in the Caputo–Fabrizio sense. The obtained approximate solutions are compared with other available solutions from existing methods by using graphical representations and numerical computations. The results reveal that the proposed method is most suitable in terms of computational cost efficiency, and accuracy which can be applied to find solutions of nonlinear fractional reaction–diffusion equations.

In this study, we perform a dynamical analysis of a generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand the dynamics of tumor development and to evaluate potential treatments. The Caputo fractional-order derivative is a mathematical tool that is recently being applied to model biological systems, including tumor growth. We present a detailed mathematical analysis of the generalized tumor model with the Caputo fractional-order derivative and examine its dynamical behavior. Our results show that the Caputo fractional-order derivative provides a more accurate description of the tumor growth dynamics compared to classical integer-order derivatives. We also provide a comprehensive stability analysis of the tumor model and show that the fractional-order derivative allows for a more nuanced understanding of the stability of the system. The least-square curve fitting method fits several biological parameters, including the fractional-order parameter $\alpha$. In conclusion, our study provides new insights into the dynamics of tumor growth and highlights the potential of the Caputo fractional-order derivative as a valuable tool in biomedical research. The results of this study shall have significant implications for the development of more effective treatments for tumor growth and the design of more accurate mathematical models of tumor development.

This consideration highlights the belongings of momentum, entropy generation, species and thermal dissemination on boundary layer flow (BLF) of Casson liquid over a linearly elongating surface considering radiation and Joule heating effects significant. Transportation of thermal and species are offered by using the temperature-dependent models of thermal conductivity and mass diffusion coefficient. Arising problem appear in the form of nonlinear partial differential equations (NPDEs) against the conservation laws of mass, momentum, thermal and species transportation. Appropriate renovation transfigures the demonstrated problem into ordinary differential equations. Numerical solutions of renovated boundary layer ordinary differential equations (ODEs) are attained by a proficient and reliable technique namely optimal homotopy analysis method (OHAM). A graphical and tabular interpretation is given for convergence of analytic solutions through error table and flow behavior of convoluted physical parameters on calculated solutions are presented and explicated in this examination. Reliability and effectiveness of the anticipated algorithm is established by comparing the results of present contemplation as a limiting case of available work, and it is found to be in excellent settlement. Decline in fluid velocity and enhancement in thermal and species transportation is recorded against the fluctuating values of Hartman number. Also reverse comportment of Prandtl number and radiation parameter is portrayed. Moreover, it is conveyed that supplementing values of the magnetic parameter condenses the fluid velocity and upsurges the thermal and concentration distributions. Negative impact of elevating Joule heating phenomenon is noted on the molecular stability of the system via Brinkman number $$\left( {Br} \right).$$Br. Furthermore, the system’s stability at a molecular level is controlled by diminishing values of radiation $$\left( R \right),$$R, temperature difference $$\left( { \in_{1} } \right),$$∈1, concentration difference $$\left( { \in_{2} } \right),$$∈2, diffusion parameters $$\left( { \in_{3} } \right)$$∈3 and Brinkman number $$\left( {Br} \right).$$Br.