Vol. 15, No. 3 (2026): Regular Issue

The thermal-hydrodynamic behavior of Bingham plastic fluids in confined systems has continued to remain a critical challenge for a wide variety of industrial applications-from polymer processing to oil drilling. Past studies have concentrated on isothermal squeeze flows and did not, however, comprehensively quantify the coupled effects associated with temperature-dependent viscosity, pressure gradients, and plate motion. The complete formulation of semi-analytical unification is presented here, in which the governing equations of nonlinear momentum and energy have been solved for the two important cases: (1) stationary parallel plates under squeezing flow and (2) moving plates with opposing velocities. Dimensionless velocity ($\overline{V}$), pressure ($\overline{P}$) and temperature ($\overline{T}$) profiles have been derived using the R.K. Fehlberg method validated through parametric analysis. The key results reveal that pressure gradients ($P$) dominate flow symmetry, with $\overline{U}$ peaking at 3.0 for $P=3$, while negative gradients induce flow reversal ($U=-2.08$ for $P=-2$), critical to avoiding particle settle in drilling muds. This is important to avoid particle settling in drilling muds. The temperature distributions lead to an average temperature drop achieved of 25% ($\overline{T}_m$) for the peclet numbers of $Pe > 10$, thus enabling better control of temperature during extrusion. Industrially, our model predicts a reduction 30% in extrusion defects under pressure differentials below 0.5 MPa. Bridging rheology theory with practical design, this work provides dimensionless scaling laws for optimization under confined non-Newtonian flow in energy-efficient systems.

This study presents a comparative analysis of the engineering applications of single-walled and multi-walled carbon nanotubes (SWCNTs and MWCNTs). The investigation focuses on the three-dimensional rotating flow of a nanofluid with nonlinear convection over an elongated surface. The heat transfer characteristics are examined under the influence of nonlinear radiation, an irregular heat source, and convective boundary conditions. Water serves as the base fluid, embedded with both SWCNTs and MWCNTs. Solutions are derived using the shooting technique, and the results are comprehensively displayed through tables and graphical representations. Detailed discussions of various flow field characteristics are provided. The findings indicate that MWCNTs exhibit a higher heat transfer coefficient compared to SWCNTs. Additionally, the presence of irregular heat sources enhances the temperature of the nanofluid.

In this paper, we study boundedness, persistence and rate of convergence of system of difference equations of exponential form $r_{n+1}=\frac{\lambda +e^{-(\mu r_{n}+\xi s_{n})}}{\delta +\mu r_{n}+\xi s_{n}}, \ s_{n+1}=\frac{\lambda +e^{-(\mu s_{n}+\xi t_{n})}}{\delta +\mu s_{n}+\xi t_{n}}, \ t_{n+1}=\frac{\lambda +e^{-(\mu t_{n}+\xi r_{n})}}{\delta +\mu t_{n}+\xi r_{n}},$ where $n=0, 1, 2,\cdots$ and $\lambda $, $\mu $, $\xi $ and $\delta $ are non-negative constants and the initial conditions $r_{0}$, $s_{0}$, $t_{0}$ are non-negative real values.

Lymphatic filariasis is a major cause of long-term disability worldwide, caused by infected female mosquitoes. To manage and control the disease, a deterministic model of ordinary differential equations that includes protected human and treatment compartments is developed, accounting for how access to treatment and movement between affected and unaffected areas influence disease spread. The analysis of the model is carried out by examining the computation of the basic reproduction number utilizing the Next-generation approach and the equilibrium states through the fixed-point and Lyapunov methods. The analysis established the conditions for the local and global stability of the equilibrium states. The sensitivity analysis is further performed using normalized forward sensitivity indices, Latin hypercube sampling and Partial Rank Correlation Coefficient (LHS/PRCC) techniques. The findings from the sensitivity analysis suggest that the rates at which mosquitoes bite and die influence lymphatic filariasis disease dynamics. This is supported by numerical simulation outcomes showing that increasing mosquito mortality and reducing the biting rate can significantly lower infection rates in both human and mosquito populations. It is recommended that public awareness campaigns on the use of insecticide-treated nets, indoor residual spraying, and mass drug administration be implemented to reduce the burden of lymphatic filariasis in the population.

This paper presents a novel six-dimensional (6D) chaotic dynamic system with a simple structure consisting of thirteen terms, including absolute value and hyperbolic tangent functions. The new 6D system, which lacks equilibrium points, exhibits hidden attractors and displays a range of dynamic behaviors such as chaotic, chaotic 2-torus, and hyperchaotic states. A comprehensive dynamical analysis is conducted, featuring bifurcation diagrams, Lyapunov exponents, Kaplan-Yorke dimensions, multistability, and offset boosting control. The proposed system, despite its structural simplicity, exhibits intricate chaotic dynamics, making it suitable for various practical applications.

The importance of the Allee effect in studying extinction vulnerability is widely recognized by researchers, and neglecting it could adversely impact the management of threatened or exploited populations [1]. In this article, we examine a discrete predator-prey model where the prey population is associated with two component Allee effects. We derive sufficient conditions for the existence and local stability nature of the fixed points of the system. The occurrence of Neimark-Sacker bifurcation is established, and sufficient conditions are obtained along with the normal form. Numerically, we demonstrate that the system exhibits Neimark-Sacker bifurcation for various system parameters. Additionally, the numerical simulations indicate that certain system parameters have threshold values, above or below which the populations are driven to extinction due to the impact of the double Allee effect.

This article investigates the mathematical models of amperometric biosensors. The given models is constructed which depends on diffusion equations of the non-linear element pertaining with an enzyme process. The approximate analytical solutions for both time - independent and time - dependent conditions of concentrations are provided in non-dimensional and dimensional for all values of the parameters. The semi-analytical expressions for the substrate, product concentrations and current are attained by utilising the new homotopy perturbation method (NHPM). The new homotopy perturbation technique is employing to solve the biosensors models like non-linear reaction-diffusion model in amperometric biosensors, potentiometric biosensors and michaelis-menten kinetics. On comparing the numerical simulation with our findings, a good fit is reached. The impacts of several parameters, including the Thiele modulus, saturation parameter, maximal enzymatic rate, the ratio of diffusion coefficients, Michaelis constant, substrate concentration in the bulk solution and thickness of the enzyme membrane are graphically represented for concentration and current.

The present study examines the unsteady MHD flow of nanofluid consisting of silver and titanium dioxide nanoparticles dispersed in water over a rotating semi-infinite vertically moving permeable plate with magnetic field, buoyancy effect, Dufour effect, viscous dissipation and Soret effect under constant heat source. The core governing relations are made dimensionless with suitable non-dimensionless variables, and the resulting consequent equations are solved by Galerkin FEM. The graphical representations depicting concentration, temperature, and velocity profiles for various different parameters are incorporated. Nusselt number; skin friction, and Sherwood numbers are also tabulated. The velocity profile accounts for increased Dufour effect, Eckert number, and Soret effect, while the trend of decreasing is reversed for increased rotation parameter. Concentration profile enhances for intensified Soret number. The study also reveals that Nusselt number declines for the suction parameter, the Sherwood number appends for the Soret number, & also the chemical reaction parameter. The study of MHD rotating vertical moving plates has potential applications in energy systems, fusion reactors, industrial coolants, and biomedical devices.

The primary focus of this article is to examine the nonlinear forced vibrations of cylindrical shells made of bidirectional functionally graded porous (BDFGP) material. These shells are surrounded by elastic foundations and subjected to a thermal environment. BDFGP shell properties are assumed to be temperature-dependent and change continuously in terms of thickness and length. The governing equations are derived based on the first-order shear deformation theory (FSDT) and the von Kármán strain-displacement relations to analyze the system's dynamic behavior. These equations describe the transverse motion of the shell. The Galerkin discretization method is then applied to obtain the final governing equation for the structure's transverse motion. The multiple time scales method is utilized to solve the governing equation and determine the nonlinear frequency response of the shell. This method provides an equation that allows for the calculation of the nonlinear frequency response. In order to validate the accuracy of the obtained results, the system frequencies are computed under various conditions and compared with the findings of previous studies. Once the accuracy is confirmed, a parametric study is conducted to assess the impact of different parameters on the nonlinear frequency response of the BDFGP cylindrical shell.

In the present work, we systematically derive the invariant subspaces for nonlinear time-fractional differential equations in the Hilfer sense and illustrate its applicability through physically significant equations such as the time-fractional heat equation, time fractional Burgers equation, time fractional KdV equation, and time fractional Hunter Saxton equation in the Hilfer sense. We also propose the invariant subspace method to time-space fractional partial differential equations involving the one-dimensional fractional Laplacian. We consider the representation of fractional Laplacian as self-induced one-dimensional Riesz potential. Our investigation reveals that linear fractional partial differential equations with the one-dimensional Riesz potential admit the exponential type invariant subspaces. Furthermore, we explore various forms of quadratic nonlinear fractional differential equations that admit the exponential invariant subspaces.

The dynamics of the predator-prey system with hyperbolic mortality subject to Neumann boundary conditions are investigated. Stability of the positive equilibrium have been discussed through distribution of the eigenvalues. With different initial values, rich spatial patterns in Turing-Hopf domain are obtained. Especially, the labyrinthine-like patterns are also discovered close to the codimension two Turing-Hopf bifurcation point under suitable conditions.

A new seven-term 4D hyperjerk system is derived from a homogeneous fourth-order differential equation. This system incorporates cross-product and cubic nonlinearities, resulting in a chaotic attractor. Its dynamic behavior is analyzed through numerical simulations and analytical studies, employing phase portraits, Lyapunov exponents, and the Kaplan-Yorke dimension. Additionally, an electronic circuit representation of the proposed system is designed using Multisim 14.3 software, with observations performed via an oscilloscope and a Tektronix oscilloscope. Numerical simulations confirm the accuracy of the electronic circuit, demonstrating strong consistency with results obtained using MATLAB 23 software. Lastly, the NIST statistical test (SP800-22) is applied to the generated chaotic sequences.

This work conducts a detailed exploration of exact wave solutions for higher-dimensional Boussinseq-Kadomtsev-Petviashvili (KP) model. By utilizing the improved modified extended tanh-function (IMETF) technique, we derive analytical solutions to the governing equation which describes the wave propagation in fluid dynamics. These solutions include dark, bright, and combined bright-dark solitons, as well as rational, exponential, singular periodic, Jacobi elliptic, and Weierstrass elliptic doubly periodic solutions. Graphical representations are provided to highlight the physical characteristics of the results.

In this paper, we use the averaging theory of first order to study the periodic solutions of the perturbed ninth-order non-autonomous differential equation $x^{(9)}-\lambda x^{8}+\psi x^{(7)}-\lambda \psi x^{(6)}+\phi\overset{.....}{x}-\lambda \chi \overset{....}{x}+A(\overset{...}{x}-\lambda \overset{..}{x})+p^{2} b^{2}( c^{2}x-c^{2})=\varepsilon \tilde{F}$ where $\tilde{F}=F(t,x,\overset{.}{x},\overset{..}{x},\overset{...}{x},\overset{....}{x},x^{(5)},x^{(6)},x^{(7)},x^{(8)}), \psi=p^{2}+b^{2}+c^{2}+1$, $\phi=p^{2}c^2+p^{2} b^{2}+b^{2}c^{2}+p^{2}+b^{2}+c^{2}$, $A=p^{2}b^2+p^{2}c^{2}+b^{2} c^{2}+p^{2}b^{2}c^{2},$ with $b$, $c $ and $p$ are rational numbers different from $-1$, $0$, $1$, and $p\neq \pm b ,$ $p\neq \pm c ,$ $b \neq \pm c $, $\varepsilon $ is sufficiently small and $F$ is a nonlinear non-autonomous periodic function. We present some applications to illustrate our main results.

The accuracy of UAV deployment is influenced by operational techniques, flight conditions, and environmental factors (e.g., altitude, speed, wind speed). This paper conducts research using kinematics, aerodynamics, differential equations, and optimization methods. A 3D coordinate system and differential equation system are established to analyze the relationship between deployment distance and key factors, with distances calculated under three wind directions (0${^\circ}$, 90${^\circ}$, 180${^\circ}$). Based on kinematics and aerodynamics, a model with four variables (launch distance, altitude, dive angle, landing time) is built. Using linear programming combined with entropy weight method, the optimal strategy is obtained: dive angle 3${^\circ}$, launch distance 1005.01 m, flight altitude 717 m, landing time 10.9 s. Introducing dive/roll angles as attitude parameters, a target programming model solved by genetic algorithm yields optimal angles (2.56${^\circ}$, 3.48${^\circ}$). Verified via Lyapunov function and regression ($R^2=0.8388$), the random forest model achieves a higher $R^2$ of 0.9899.

In this paper, we present a study on the dynamics of knowledge acquisition in learning environments. We utilized compartmental models to investigate the complex factors influencing knowledge dissemination within academic settings. Our analysis included estimating the basic reproduction number, analyzing the equilibria, and assessing the stability of the models. We also conducted sensitivity and bifurcation analyses of the proposed model. Finally, we presented numerical simulations to highlight the outcomes of our analytical work.