Narrow Results

The aim of this work is to develop a model of alcohol that takes drug features into account. We assess the model feasibility and explain its formulation in terms of a nonlinear differential equation. Using the subsequent matrix generation technique, we ascertain the reproductive number in order to assess the dynamics of the model. We also examine the system equilibrium points, namely the positive and free alcohol equilibrium points. To gain insights into the stability properties of the model, we utilize the Lyapunov function and the Routh–Hurwitz criterion. Through these methods, we investigate both the local stability and global stability of the considered model. Furthermore, we employ numerical simulations to complement and illustrate the theoretical results obtained. These simulations provide visual representations that enhance the understanding of the model dynamics and behavior.

Our main interest in this study is to obtain approximate time-dependent solutions of the Lotka–Volterra predator–prey model given the populations of both species at a certain time. We achieve this by considering an earlier scheme by Shinohara and Yamamoto and modifying it so as to address the initial conditions. An important feature of this scheme is that it treats the system’s period as an unknown variable, making it possible to calculate it as a side product. In this method, the Galerkin procedure is utilized to convert the problem to a system of nonlinear algebraic equations, where sine and cosine waves are chosen as the basis functions in order to ensure the periodicity of solutions. The resulting overdetermined system is then solved in a least squares sense, which yields the coefficients making up the Galerkin approximations. After a detailed presentation of the numerical scheme, we apply it to two example problems and evaluate the results according to several accuracy criteria.

Carbon nanotubes (CNTs) influenced nanofluid is gaining popularity in the industry for solar energy and scratch heat exchanger applications. Consequently, this research focuses on evaluating the impact of nonlinear thermal radiation from a CNT-based nanofluid on an unsteady three-dimensional nonasymmetric Homann stagnant flux as a function of length and radius. CNTs have remarkable thermal physical properties that appear to be critical for nonlinear thermal transport. As a result, the nonlinear heat transfer properties of H₂O composed of single or multiple wall CNTs are studied. The nanomaterial has a length and radius of approximately $3\mathrm{\text{nm}}\le L\le 70\mathrm{\text{nm}}$ and $10\mathrm{\text{nm}}\le R\le 40\mathrm{\text{nm}}$. Partially differential equations with appropriate similarity transformations serve as a mathematical model for the process. The numerical solution of the simplified system of equations is achieved via the use of the well-known Runge–Kutta (RK) method in conjunction with the shooting approach. An effective way to show how a component affects velocity and temperature, skin frictions in both direction and Nusselt number are utilized in graphical representations. Increasing the unsteadiness parameter causes a reduction in the temperature profile and the velocity profile in both directions. As $\epsilon$ grows larger with $\varphi$, the skin friction in both directions decreases, while the Nusselt number profile grows larger. In addition, the variation in the Nusselt number is included in the tables, along with a comparison of the model without radiation to the model with radiation.

We investigate solutions to the Klein–Gordon equation in a class of five-dimensional geometries presenting the same symmetries and asymptotic structure as the Gross–Perry–Sorkin monopole solution. Apart from globally regular metrics, we consider also squashed Kaluza–Klein black holes backgrounds.

Recent results show that when nonlinear electrodynamics is considered, the no-scalar-hair theorems in the scalar–tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented.^1,2 What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to nonlinear electrodynamics in a special class of scalar–tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar–tensor theories considered, the black holes have a single, non-degenerate horizon, i.e. their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicates that a phase transition may occur.

In this work, a Liouville–Caputo fractional order (FO) derivative for the mathematical system based on the accelerating universe in the modified gravity (AUMG), i.e. FO-AUMG is proposed to get more accurate solutions. The nonlinear dynamics of the FO-AUMG is classified into five dynamics. The performances of the designed nonlinear FO-AUMG are numerically stimulated with the stochastic procedures of Levenberg–Marquardt backpropagated (LMB) scheme-based neural networks. The statics for FO-AUMS is used for the nonlinear FO-AUMG as 72%, 16% and 12% for training, authorization, and testing. Twenty neurons in hidden layers have been used to approximate the solution of the nonlinear FO-AUMS. The comparison of three different cases of the nonlinear FO-AUMS is performed with dataset generated by Adams method. To validate the uniformity, legitimacy, precision, and competence of LMB-based adaptive neural networks, the outcomes of the state transitions parameters, regression, correlation, error-histogram plots have been exploited.

In this paper, the new traveling wave solutions containing the trigonometric functions, hyperbolic functions and rational functions of $(3+1)$-dimensional Zakharov–Kuznetsov equation are obtained. The graphs of the solution functions are presented by giving specific values to the constants. Numerical solutions are obtained by using finite difference method with new initial condition. Von Neumann’s Stability, Consistency and Linear Stability analysis of the equation are performed and $L_2$, $L_{\infty }$ norm errors are also examined with the truncation error. The exact solution obtained is presented via numerical solutions and absolute error graphs, and the analysis of exact solution and the numerical solutions are performed. Complex operations and graphical drawings were made using the computer package program.

Mathematical modeling plays a crucial role in understanding the dynamics of Human immunodeficiency virus (HIV) disease. Most models deal with the vertical and horizontal spread of disease, but few studies have focused on the evolutionary dynamics of HIV at the cellular level. In this paper, we present an HIV model to analyze the dynamics of HIV infection at the cellular level to produce more natural results. We present a detailed stability analysis of disease-free and viral-persistence equilibrium in the system. In addition, sensitivity analysis and optimal control strategies are used to analyze the role of antiretroviral drug therapy and dietary supplements in controlling the concentration of infected cells and viruses.

In this paper, with the help of a computer package program, the auto-Bäcklund transformation method (aBTM) and the finite forward difference method are used for obtaining the wave solutions and the numeric and exact approximations to the FitzHugh–Nagumo (F-N) equation, respectively. We successfully obtain some wave solutions to this equation by using aBTM. We then employ the finite difference method (FDM) in approximating the exact and numerical solutions to this equation by taking one of the obtained wave solutions into consideration. We also present the comparison between exact and numeric approximations and support the comparison with a graphic plot. Moreover, the Fourier von-Neumann stability analysis is used in checking the stability of the numeric scheme. We also present the $L_2$ and $L_{\infty }$ error norms of the solutions to this equation.

This paper focuses on realizing the exact solutions of three distinct important biological models using the Painlevé approach. These three models are the nonlinear dynamics of microtubules — a new model, the Kundu–Eckhaus model and the double chain model of DNA. Furthermore, the numerical solutions of these three equations have been achieved using the variational iteration method.

The main goal of this study is to find solutions for the generalized coupled Ramani equation with the fractional order using the fractional natural decomposition method (FNDM). Four distinct cases are chosen to illustrate and validate the effectiveness of the considered method. The simulations in terms of numeric have been illustrated to confirm the reliability and proficiency of the projected scheme. Moreover, the behavior of the obtained results is captured for distinct fractional order. The comparison study is illustrated to verify the accuracy of the projected procedure. The achieved results exemplify that the projected solution procedure offers a simple algorithm and is also very efficient to analyze the nature of the coupled differential equations with arbitrary order situated in associated areas of Science and Engineering.

This paper analyzes the analytical and numerical solutions’ structure of the combined mKdV equation and KdV equation (mKdV+KdV equation) using the Khater II (Khat. II) method and three accurate B-spline numerical schemes. ExCBS, SBS and TQBS numerical schemes are the numerical systems used. The handled model describes many distinct phenomena such as wave propagation of bounded particles with a harmonic force in a one-dimensional nonlinear lattice, propagation of ion-acoustic waves of small amplitude without Landau damping in plasma physics, and propagation of thermal pulse through a single sodium fluoride crystal in solid physics. Numerous examples show the relationship between quick and slow soliton, which generates phase shift. This phase shift is shown in a contour map to show the modest and colossal energy density along the path of fast and slow colliding solitons. Calculating the difference between analytical and numerical solutions shows whether they match spline-connected and distribution graphs.

Approximation and analysis are used for investigating accurate soliton solutions of the ill-posed Boussinesq (IPB) equation. The investigated model explains shallow-water gravitational waves. It examines one-dimensional nonlinear strings and lattices. IPB explains small-amplitude surface waves on nonlinear strings and lattices. We provide unique analytical solutions to analyze numerical beginning and boundary conditions. A solution’s quality is judged by its divergence from analytical predictions. Physical wave properties are illustrated.

The increasing number of ways in which carbon nanotubes (CNTs) may be used in business and technology has led to an explosion of interest in these tiny tubes. As a result, the Yamada–Ota model is used to investigate the unsteady, non-axisymmetric MHD Homann stagnation point of carbon nanotubes passing over a convective surface with nonlinear radiation. Consisting of single-walled and multi-walled carbon nanotubes that are suspended in water (H₂O). The length of the nanomaterial is between $3\mu \mathrm{\text{m}}\le L\le 70\mu \mathrm{\text{m}}$ nanometers, while its radius is between $10\mathrm{\text{nm}}\le R\le 40\mathrm{\text{nm}}$. The method of similarity transformation is altered so that it may be used to get the dimensionless system of differential equations from the mathematical model that is envisioned for PDEs. After that, approximate solutions are obtained using MATHEMATICA and the Shooting with RK-IV technique. In this paper, we provide a graphical discussion and a physical interpretation of the results of measures of practical significance as a function of key factors. The results indicated that an increase in the volume fraction led to a corresponding rise in the heat transfer rate. However, it is reduced by the magnetic energy that is supplied to it. Carbon nanoliquids with a single wall have a greater melting point than nanoliquids with multiple walls. Industrial and technological uses of the issue under examination span several fields, including aviation and health. The results of the interface velocity and heat transfer rate at the surface, as well as the solution of each profile, are shown graphically, along with an analysis of the effects of MHD on the flow and heat transfer characteristics of the fluid under the influence of radiation.

A hydro-dynamic thermal fully developed forced convective heat transfer analysis of magneto-hydrodynamics fluid flow through an annular sector duct is presented in this paper. Two types of thermal boundary conditions i.e., axially uniform heat flux along with peripherally uniform temperature (known as H1-condition) and, axially and peripherally uniform temperature (known as T condition), have been considered to carry out the thermal analysis of fluid. The velocity components along r and $\theta$ direction are transformed into algebraic form by using power law discretized scheme, whereas cross-sectional pressure $P(r,\theta )$ is estimated with the help of well know technique $SIMPLER$. The governing partial differential equations are solved by numerically with the help of $MATLAB$ code. Furthermore, simulated results have been compared with the existing results of literature to validate the results. From the results, it is noted that hydro-dynamically and thermally impacts relate directly by increasing the Hartman number, (M). It is further reported that the effect of magnetic field becomes insignificant for the higher number of fins, N. The findings of the present analysis will be applicable in various types of thermal systems.

In this paper, the stable analytical solutions’ accuracy of the nonlinear fractional nonlinear time–space telegraph (FNLTST) equation is investigated along with applying the trigonometric-quantic-B-spline (TQBS) method. This investigation depends on using the obtained analytical solutions to get the initial and boundary conditions that allow applying the numerical scheme in an easy and smooth way. Additionally, this paper aims to investigate the accuracy of the obtained analytical solutions after checking their stable property through using the properties of the Hamiltonian system. The considered model for this study is formulated by Oliver Heaviside in 1880 to define the advanced or voltage spectrum of electrified transmission, with day-to-day distances from the electrified communication or the application of electromagnetic waves. The matching between the analytical and numerical solutions is explained by some distinct sketches such as two-dimensional, scatter matrix, distribution, spline connected, bar normal, filling with two colors plots.

This study focuses on the analysis of peristaltic transport of a hybrid nanofluid comprising deionized water as a base fluid and the multi-walled carbon nanotubes (MWCNTs) and copper oxide (CuO) as nanoparticles within a sinusoidal wavy porous duct, taking into consideration the influence of heat generation or absorption. The inaugural literature piece addresses the utilization of hybrid nanofluid in the context of peristaltic flow within ducts. To simplify the analysis, we have converted the non-dimensional equations into a two-dimensional (2D) coordinate system using the assumptions of a very long wavelength $(\delta <1)$ and low Reynolds number (Re). The non-dimensional equations governing the behavior of the hybrid nanofluid are then solved numerically using the finite volume method. Numerical solutions for temperature and the 2D peristaltic flow are obtained with the assistance of the Mathematics software MATLAB. These solutions are subsequently represented graphically using MATLAB software. The graphical results highlight several key findings for important parameters. First, it is observed that the pressure rise, temperature profile, and pressure gradient in the hybrid nanofluid (CuMWCNTs/H₂O) flow increases as heat generation increases. Furthermore, an increase in the nanoparticle volume fraction of both nanoparticles leads to a decrease in the pressure rise and pressure gradient in the hybrid nanofluid flow. Additionally, the widening of the channel reduces the pressure gradient and pressure rise in the CuMWCNTs/H₂O hybrid nanofluid. The analysis also includes the visualization of streamlines for peristaltic transport. These streamlines reveal that an increase in amplitude results in larger bolus sizes, while heightened heat generation has the opposite effect, decreasing bolus sizes. The results of this investigation can be found in various cooling devices as flows in the ducts are very frequently utilized for the cooling process of engines. A further topic is common in applications related to microfluidics, heat exchangers, and biomedical devices where peristaltic pumping is employed. Our results are in 100% agreement with the existing literature in special cases.

We study five-dimensional black holes in Einstein–Maxwell–Chern–Simons theory with free Chern–Simons (CS) coupling parameter. We consider an event horizon with spherical topology, and both angular momenta of equal magnitude. In particular, we study extremal black holes, which can be used to obtain the boundary of the domain of existence. Above a critical value of the CS coupling constant we find nonstatic extremal solutions with vanishing angular momentum. These solutions form a sequence which can be labeled by the node number of the magnetic U(1) potential or the inertial dragging. As the node number increases, their mass converges to the mass of the extremal Reissner–Nordström solution. The near-horizon geometry of the solutions of this sequence is the same. In general not all near-horizon solutions are found as global solutions, and we show nonuniqueness between extremal solutions and nonextremal ones.

We review recent results on the existence of static black holes (BHs) without spatial isometries in four spacetime dimensions and propose a general framework for their study. These configurations are regular on and outside a horizon of spherical topology. Two different mechanisms allowing for their existence are identified. The first one relies on the presence of a solitonic limit of the BHs; when the solitons have no spatial isometries, the BHs, being a nonlinear bound state between the solitons and a horizon, inherit this property. The second one is related to BH scalarization, and the existence of zero modes of the scalar field without isometries around a spherical horizon. When the zero modes have no spatial isometries, the back-reaction of their nonlinear continuation makes the scalarized BHs inherit the absence of spatial continuous symmetries. A number of general features of the solutions are discussed together with possible generalizations.

In this work, we investigate a nonlinear fractional order Lotka–Voltera prey–predator model. It is also worth mentioning that we develop some results about the existence of the solution through fixed point theory. After investigating the existence results, we also develop a suitable technique with the help of Laplace transform coupled with Adomain decomposition in order to obtain the approximate solutions for the underlying model. Here, it should be kept in mind that we study the proposed model subject to variable coefficients. The results obtained via the aforesaid techniques are illustrated graphically via Matlab-16 corresponding to different fractional order by taking two cases.

Reviewers list:

• Prof. Dumitru Baleanu (Cancaya University Ankara Turkey), Email:

  E-mail Address: dumitru@cankaya.edu.tr

  ,
• Dr. Anwar Zeb (COMSAT, University Pakistan), Email:

  E-mail Address: anwar@cuiatd.edu.pk

  ,
• Prof. J. F. Gómez-Aguilar (CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C. P. 62490, Cuernavaca, Morelos, México), Email:

  E-mail Address: jgomez@cenidet.edu.mx

  .