Vol. 15, No. 4 (2026): Regular Issue

This paper presents a novel VSEITR fractional-order model to investigate the dynamics and control strategies of tuberculosis (TB) in Algeria. The model incorporates the Caputo fractional derivative, offering a more precise representation of TB transmission dynamics by integrating memory effects and long-term dependencies. Using TB data reported from 1990 to 2023, the model parameters were carefully calibrated, demonstrating a strong alignment with real-world data. Key analyses include the computation of the basic reproduction number, $\mathcal{R}_0$, and the examination of equilibrium states. Stability of both disease-free and endemic equilibria are rigorously analysed within the fractional model. Numerical simulations highlight the advantages of the proposed fractional-order model in capturing complex disease behaviour, with implications for public health strategies.

This paper presents the development of a Finite-Time Disturbance Observer-Based Sliding Mode Controller (FTDOBSMC) for controlling and stabilizing a Rotary Inverted Pendulum (RIP) system. The FTDOBSMC is composed of three key elements: a finite-time disturbance observer for estimating disturbances, a nonlinear sliding surface designed to enhance convergence speed during the sliding motion phase of sliding mode control, and a Combinatorial Reaching Law (CRL) that integrates the power reaching law and the variable speed reaching law. This combination helps minimize chattering and improve system robustness. The stability of the RIP system is validated using Lyapunov theory. Notably, simulation results demonstrate that the FTDOBSMC achieves faster convergence of the closed-loop system to the origin, maintains the pendulum angle closer to the stable equilibrium point, and exhibits superior robustness against various types of time-varying disturbances.

We derived an approximate analytical solution of the coupled highly nonlinear equation by a newly proposed method of directly defined inverse mapping (MDDiM) and analytically by Cardan's method to the boundary value problem bringing out the effects of important parameters. Then we considered the hydromagnetic flow of Oldroyd-B Model, (an experimentally supported realistic fluid model) through a vertical channel with both electrically conducting and non-conducting walls having asymmetric wall temperatures. The viscoelastic flow subjected to the transverse magnetic field with Hall current and induced magnetic field (IMF) considered. Subsequently, for engineering interest, the skin friction, mass flux and induced current density for relevant parameters were analyzed. The Mathematica 10.0 software is used for plotting graphs and tables. The novel findings reported here in may be useful in the design of heat ex-changers. There exists a threshold value of the Hall parameter when it is exceeded, flow reversal occurs; the primary as well as magnitude of secondary velocity increase with the higher values of stress relaxation time; the effects of strain retardation time on velocity component and It is seen that the Hall current enhances the velocity at all points in the flow domain, whereas, the Hartman number reduces it, it is revealed that the secondary velocity profile has an inverted structure with a sharp increase in magnitude of $u_{y} $ for an increase in Hall current, whereas in the case of primary velocity, no flow reversal is marked. An opposite effect is marked with reference to stress relaxation time.

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 theory of natural evolution and computations has contributed to many advancements in science and engineering. Consequently, this article explores the analytical examinations of a new integrable (1+1)-dimensional Boussinesq equation recently formulated in the literature which is applicable in optics, fluid dynamics, ocean science and other nonlinear sciences and engineering. Lie group theory in differential equations is then applied to identify point symmetries within the model, enabling the derivation of nonlinear ordinary differential equations through symmetry reductions. In addition, direct integration is invoked to secure some soliton solutions, such as bright, periodic, and singular. More importantly, the Jacobi elliptic function approach is further engaged to secure abundant general exact travelling wave solutions in the structures of periodic as well as singular soliton solutions to the model. This technique enables the attainment of various exact soliton solutions, including topological and non-topological soliton solutions (both complex and non-complex). Additionally, general periodic function solutions of note, such as cosine amplitude, sine amplitude, and delta amplitude solutions of the model, are also secured. In the same vein, a power series approach is utilized to solve part of the difficult nonlinear ordinary differential equations obtained. Besides, by taking some essential limits of part of the solutions, one obtains various soliton results, including triangular solutions of the understudy model. These are in the form of hyperbolic and trigonometric functions, achieved with regards to the secant, tangent, and cotangent functions. Furthermore, numerical simulations of the solutions are invoked to gain a gross knowledge of the physical phenomena represented by the understudy integrable Boussinesq equation. Conclusively, the study further produces conserved quantities of note, such as energy, mass, and momentum, which are secured through the use of Ibragimov's theorem, as well as the multiplier approach.

The purpose of this study is to explore the dynamical behaviour of a predator-prey environment that incorporates Allee effects in prey, group defence, and supplemental food for the predator, while taking into account both delayed and stochastic factors. Two nonlinear differential equations make up the deterministic model. In this model, the population of prey is characterised by Allee effects and group defence, while the predator is able to reap the benefits of an alternative food supply. The model also takes into account the temporal delay in the reproduction of predators, which allows it to capture the influence that the availability of prey in the past has on the expansion of predators. By incorporating Gaussian white noise disturbances into the prey and predator populations, the system is expanded to a stochastic framework, which takes environmental fluctuations into consideration. Our analysis consists of a study on the stability of equilibrium points, the derivation of Hopf bifurcation conditions due to delay, and an investigation into the effects that noise has on the persistence and extinction of populations. The current work provides a thorough integration of these mechanisms into a single framework, in contrast to earlier research that looked at discrete elements like the Allee effect, temporal delay, or stochasticity in isolation. To verify the theoretical findings and illustrate the intricate interaction between deterministic, delayed, and stochastic elements in influencing predator-prey dynamics, numerical simulations are utilised. The results offer important new information for managing ecosystems and conserving biodiversity in settings that are prone to natural oscillations.

Capsule robots (capsubot) are increasingly used in endoscopic operations, diagnostics, drug delivery, and the treatment of gastrointestinal diseases. In addition to meeting size requirements, the capsubot must be capable of controlling its movement within the digestive tract. This paper proposes a new model of a self-moving capsule device that exploits the vibro-impact effect, accounting for the influence of viscous resistance in the gastric digestive fluid environment. Adding the viscous resistance component $F_{D}$ will take into account the influence of factors such as liquid viscosity, density, liquid flow velocity and the size of capsule. The XPPAuto numerical simulation tool is used to determine the numerical solution for the mathematical model and evaluate the performance of the capsubot in gastric fluid. Numerical analysis results show that the impact gap (G), frequency (f), amplitude ($i_{0}$), and duty cycle (pulse width) of the stimulation signal significantly affect the capsubot's direction and displacement. These findings can be used to optimize control variables and design parameters, forming a foundation for building an experimental system to verify and evaluate the capsubot system's dynamic behavior. This approach also helps reduce time and costs in designing and manufacturing experimental models for developing active capsules.

Two novel phenomena for unidirectionally coupled $3$-cell Hopfield neural networks (HNNs) are investigated. The first one is the persistence of chaos, which means the permanency of sensitivity and infinitely many unstable periodic oscillations in the response HNN even if the networks are not synchronized in the generalized sense. The doubling of chaotic attractors is the second phenomenon realized in this study. It can be achieved when the response network possesses two stable point attractors in the absence of the driving. This feature leads to the formation of two coexisting chaotic attractors with disjoint basins. Lyapunov functions are utilized to deduce the presence of an invariant region, and the sensitivity is rigorously proved. The absence of synchronization is approved via the auxiliary system approach and analysis of conditional Lyapunov exponents. Additionally, quadruple and octuple coexisting chaotic attractors are demonstrated, and the formation of hyperchaos is discussed.

This research investigates the Darcy-Forchheimer flow of a non-Newtonian Eyring-Powell nanofluid containing copper nanoparticles. The physical configuration for the mathematical model is based on the Riga plate. The heat transfer rate of the fluid model is enhanced by utilizing the Cattaneo-Christov model in combination with the heat and mass equations. The system of partial differential equations governing the flow is converted into a system of ordinary differential equations through similarity transformations. The MATLAB bvp4c technique is employed to obtain numerical solutions, while the Homotopy analysis method is utilized to derive analytical solutions. The results of numerical and analytical methods are compared in tabular form. The graphical results of various physical quantities with different parameters are presented. It has been observed that the higher radiation and heat generation parameters increase the temperature of the fluid. The concentration profile is enhanced with the greater chemical reaction parameter and Schmidt number. As the temperature distribution parameter increases, the skin friction coefficient increases, while the Nusselt number and Sherwood number decline with the greater radiation parameter and the chemical reaction parameter, respectively. The Nusselt number increases when the heat absorption parameter varies from 0.0 to 6.0, and a decline in the Sherwood number is observed as the Schmidt number varies from 0.0 to 0.6 for Eyring-Powell fluids.

Mathematical modelling of blood flow through a patient-specific atherosclerotic artery has been developed in the present study. The blood flow within the arterial lumen is assumed to behave as a non-Newtonian Casson fluid. An external transverse magnetic field is applied to the flowing blood. The nonlinear coupled governing equations, along with the relevant initial and boundary conditions, are solved numerically using the MAC (Marker and Cell) method, satisfying suitable stability criteria. The effects of the external magnetic field (Hartmann number) on the axial velocity, wall shear stress, and pressure are shown graphically. Significant effects of Reynolds number and yield stress on both axial velocity and wall shear stress have also been observed. The present study also investigates the significant effect on the velocity profile in the presence of an external magnetic field. The simulated results indicate that the dimensionless centreline velocity is higher for the Newtonian model compared to its non-Newtonian counterpart. The predicted results agree well with the results available in the literature.

This article explores the intricate dynamics of incommensurate chaotic systems involving the Caputo fractional derivative as fractional dynamics are particularly suited for capturing complex behaviors in real-world nonlinear systems with memory properties. Initially, we provide Hopf bifurcation analysis which indicates insights into the rich temporal evolution and nonlinear dynamical behavior of these systems. Further, a fractional version of the Runge-Kutta method is employed for the first time to numerically analyze these systems, enabling a thorough investigation of how system parameters and fractional orders influence the emergence and transition of chaos. Numerical simulations, illustrated through phase portraits, reveal the formation of rich chaotic attractors. Additionally, We characterize the systems' stability and chaotic regimes using Lyapunov exponent computations, Poincaré sections, bifurcation diagrams, and maximum Lyapunov exponent spectra.

This work establishes new sufficient conditions that ensure all solutions are oscillatory for a class of forced nonlinear fractional partial difference equations. A key contribution of this study is the distinction between two types of boundary conditions: inhomogeneous conditions, which introduce external influences through boundary terms, and homogeneous damping-type conditions, which regulate the solution internally. These boundary conditions play a central role in shaping the qualitative behavior of solutions. The analysis is carried out using the Riemann-Liouville fractional difference operator of order $\eta\in(0,1]$, together with forcing terms that influence the system's dynamics. The results extend existing oscillation criteria to a broader class of nonlinear problems. Numerical examples are provided to illustrate and validate the theoretical findings.

In this paper, we study the problem of the prescribed-time (PT) synchronization for multiweighted directed complex networks (MWDCNs) with time-varying delays via hybrid control method. The nonlinear and coupling terms have $N+1$ non-identical time-varying delays, which increases the difficulty of our study. The network topology is not assumed to be disconnected, which implies only the outer coupling matrix is required to be asymmetric. The coupling matrix is dealt with the rearrangement of variables (ROT) method. An effective synchronization criterion is established. Finally, the effectiveness of the proposed method is illustrated by a numerical simulation.

In this paper, we have fuzzified the nonlinear mathematical model given by Devi and Mishra [1] to compare the dynamics of carbon dioxide (CO$_2$) in crisp and fuzzy environments. Reserved forestry biomass is necessary to control the dynamics of CO$_2$. Devi and Mishra [1] have studied the dynamics of CO$_2$ under a system consisting of reserved forestry biomass, unreserved forestry biomass, and human population in a crisp environment. We have analyzed the dynamics of CO$_2$ under the system consisting of reserved forestry biomass, unreserved forestry biomass, and human population in crisp and fuzzy environments. Conditions for boundedness of solutions, existence, and stabilities of equilibrium points are discussed for the fuzzified model system. We have performed numerical simulations to validate our analytical findings and to see the comparison in the dynamics of CO$_2$ between crisp and fuzzy environments. In this study, many notable differences were found in the dynamics of CO$_2$ in crisp and fuzzy environments.

This study presents a mathematical model to investigate the dynamics of malaria and typhoid co-infection, focusing on the interplay between the two diseases and their combined impact on public health. The co-infection is driven by shared social and environmental transmission factors, particularly in vulnerable populations. The equilibrium and the threshold values $R_{0_{T}}$, $R_{0_{M}}$ & $R_{0_{TM}}$ of typhoid only, malaria only, and the typhoid malaria co-infection model respectively, were resolved. The stability analysis and occurence of backward bifurcation under certain conditions have been studied. We applied major cost-effectiveness technique to determine the most cost-effective control measures. Motivated by the recent flood crisis in Delhi and the associated contamination of the Yamuna River, we estimate key transmission parameters using the least squares fitting on Delhi cases data. Our model is validated by aligning the infection curves with official government reports. Furthermore, apply the ARIMA time-series forecasting model to predict malaria trends for $2025$ and $2026$. Also, we applied sensitivity analysis to investigate the impact of one disease on the other. The results show a correlation between malaria infection and a higher risk of contracting typhoid, but not an increased risk of malaria.