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 onedimensional 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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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, 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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
In this paper, we have fuzzified the nonlinear mathematical model given by Devi and Mishra [1] to compare the dynamics of carbon dioxide (CO2) in crisp and fuzzy environments. Reserved forestry biomass is necessary to control the dynamics of CO2. Devi and Mishra [1] have studied the dynamics of CO2 under a system consisting of reserved forestry biomass, unreserved forestry biomass, and human population in a crisp environment. We have analyzed the dynamics of CO2 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 CO2 between crisp and fuzzy environments. In this study, many notable differences were found in the dynamics of CO2 in crisp and fuzzy environments. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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 is an element of (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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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 soli-ton 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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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 2torus, 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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
In this paper, we study boundedness, persistence and rate of convergence of system of difference equations of exponential form lambda + e-(& micro;rn+xi sn) rn+1 = , sn+1 = delta + & micro;rn +xi sn lambda + e-(& micro;sn+xi tn) , tn+1 = delta + & micro;sn + xi tn lambda + e-(& micro;tn+xi rn) , delta + & micro;tn +xi rn where n = 0,1, 2, & centerdot;& centerdot; & centerdot;and lambda, & micro;, xi and delta are non-negative constants and the initial conditions r0, s0, t0 are non-negative real values. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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 Karman 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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
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. (c) 2026 L&H Scientific Publishing, LLC. All rights reserved.
