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This research paper presents a comprehensive study on the intricate interplay of rotational, magnetic field and heat transfer effects in squeezing fluid flow, utilizing the foundational framework of Navier–Stokes equations. Fluid flow in confined geometries has significant applications in various industrial processes, including lubrication systems, microfluidics, and heat exchangers. The integration of rotational motion, magnetic fields, and heat transfer phenomena into this context holds immense potential for optimizing performance and efficiency. The study commences with the derivation and analysis of the coupled Navier–Stokes equations, incorporating the Coriolis force due to rotational motion, the Lorentz force arising from magnetic fields, and the energy equation for heat transfer. This comprehensive model accounts for the complex interactions between these physical phenomena, offering a holistic perspective on squeezing fluid flow dynamics. Numerical analysis are conducted to investigate the behavior of fluids under the influence of rotational, magnetic field, and heat transfer effects. The results reveal intricate flow patterns, including vortex formation and heat transfer enhancement. Furthermore, the impact of key parameters such as rotational speed, magnetic field strength, and temperature gradients on flow characteristics is systematically analyzed. The Dufour effect pertains to the transfer of energy resulting from a gradient in mass concentration, occurring as a correlated consequence of irreversible processes. It functions as the inverse of the Soret effect. The temperature changes due to the concentration gradient, amplifying as the Dufour number increases. The most significant temperature rise is observed at the midpoint of the fluid domain. Conversely, the Soret number behaves in a similar but opposite manner. Tables 4–10 has been created to offer a comprehensive analysis of the optimal alignment between Homotopy Analysis Method (HAM) and BVP4c. Specifically, it demonstrates a continuous decrease in skin friction for ξ S o , ξ R d , and ξ R 2 , while showing an increase for ξ S c , ξ D o , and ξ R e m . Meanwhile, the skin friction remains constant for ξ P r . The research centers on analyzing heat and mass transfer properties within an incompressible fluid confined between two rotating and stretching disks amidst an unpredictable flow pattern. The study employs a blend of analytical and numerical approaches to solve the governing equations, delving into the intricate fluid dynamics and the intricate processes of heat and mass transfer within this intricate system. [ABSTRACT FROM AUTHOR]

In the present work, Einstein's vacuum field equation is investigated analytically to explore the solitary wave solutions. This equation arises in mathematical physics, having meaningful applications in the general theory of relativity. This concept is crucial for numerous challenging experiments and space missions. The generalized exponential rational function and modified auxiliary equation approaches are used to obtain the exact solitary wave solution. Various types of solutions are extracted, including exponential functions, hyperbolic functions, trigonometric functions, and rational forms. Additionally, a stability analysis for the Einstein vacuum field equation is conducted. Appropriate parameters are chosen to draw 3-D and corresponding contour plots of some solutions, which clearly demonstrate the solitary wave behaviors. The obtained results support the idea that applying these approaches is the most effective strategy for resolving any nonlinear issues that may arise in science and technology. [ABSTRACT FROM AUTHOR]

In this study, we solve fractional order PDEs with free parameters that regulate wave motion in a low-pass electrical transmission line equation (LPET) using the unified technique. To convert the governing equation into an ordinary differential equation (ODE), we have used a simple linear fractional transformation. The unified technique can therefore be used to find various single and extracting wave solutions to the equation of attention. Using Maple-18 software, all of the established solutions are validated and verified. By selecting appropriate values for the fractional order and free parameters, the two dimensional (2D) and three dimensional (3D) profiles of some of the assimilation solutions demonstrating kink, singular kink, cross kink, bright-dark kink, lump type kink, anti-kink, dark-anti kink, singular periodic, periodic, singular soliton solutions are displayed. The effect of free parameters and fractionality on the dynamical properties of the precise and exploited solutions are graphically illustrated and discussed in detail. We have also compared our results to those found in the literature review. Wherever possible, the judgment demonstrates no significant differences between our realized and published solutions. The results of this investigation show that the adopting technique is both productive and powerful in extracting wave solutions to nonlinear evolution problems that arise in the areas of applied mathematics, mathematical physics, and engineering. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and assess a stochastic model for pneumonia-typhoid co-infection to investigate their distinctive correlation under the impact of preventative techniques considering environmental noise and piecewise fractional derivative operators. Initially, we conducted a descriptive investigation of the model, and the basic reproductive number is defined in terms of the existence and stability of dynamic equilibrium. Then, we obtain the sufficient requirements for the existence of an ergodic stationary distribution by utilizing a novel methodology for constructing stochastic Lyapunov candidates. Besides that, the basic stochastic reproductive R 0 s as a threshold that will examine the extinction and persistence of the disease. Through a rigorous analysis, this study presents the concept of piecewise derivative with the goal of modelling the co-dynamics of pneumonia and typhoid fever with varying kernels. We viewed various possibilities and described numerical strategies for addressing difficulties. Visual observations, such as chaotic and dynamical behaviour patterns, are provided to demonstrate the efficacy of the proposed notion. Thus, the innovative considerations of fractional calculus include more versatile configurations, allowing us to more effectively acclimate to the dynamic system behaviours of real-world manifestations. Finally, we discovered that treating pneumonia with typhoid fever preventative measures is the least expensive. As a result, for advantageous and cost-effective regulation of both pathogens, legislators must prioritize preventative measures while not overlooking treatment of affected patients. [ABSTRACT FROM AUTHOR]

The flow of temperature distribution through a medium in thermodynamic studies plays an important role in understanding physical phenomena in chemical science and petroleum engineering, while temperature distribution indicates the degree of reaction that must be undergone to obtain the final product. Therefore, this paper aims to present and apply the exponential matrix algorithm (EMA), differential transformation algorithm (DTA), and Runge-Kutta (RK5) to simulate the temperature distribution in five heating tanks in series. successive preheating of multicomponent oil solutions. A mathematical model of the energy balance equations of the reservoir is considered. Two computer experiments were performed to test and investigate the relationship between two constant parameters appearing in the model. Numerical simulation of saturated steam T steam temperature of 500 °C and 1000 °C used to heat the tanks and initial temperature T 0 35 ° C a n d 100 ° C of the first tank feed oil are considered. The fluids in the reservoirs were considered homogeneous throughout the experiment and changes in the cell configuration at two constant parameters were presented in the 2D plot control with the use of the MAPLE 18 software package. The study revealed the nature of the temperature distribution that the higher temperature distribution is obtained when heat is transferred from the first tank to the fifth tank and the reverse reaction occurs in all five reservoirs when ψ = 0.0025 and ω = 0.0025 respectively. Numerical results obtained are prototypes of oil temperature distribution performed under laboratory conditions in a thermodynamic experiment. [ABSTRACT FROM AUTHOR]

This work attempts to study the numerical solution of nonlinear delayed Immunized Susceptible Latent Infected and Recovered (MSLIR) epidemic model of HBV disease. Reproduction number, equilibria and stability are discussed. Three different numerical techniques, Euler, RK-4 and the non-standard finite difference (NSFD) techniques are used for the numerical solution of the model. The proposed technique is independent of the size of the time step, while forward Euler and RK-4 depend on the size of a time step and retains all essential characteristics of the continuous MSLIR epidemic model like positivity and stability of equilibrium, while well-known forward Euler and RK-4 cannot sustain these characteristics. Therefore, the proposed (NSFD) technique becomes a more efficient and reliable numerical technique than the forward Euler and RK-4 scheme. Numerical simulations are presented for the validation of the obtained results. [ABSTRACT FROM AUTHOR]

The one-dimensional long water wave propagation in a nonlinear medium, including the dispersion process, is well simulated by the fractional-order modified equal-width (MEW) equation. This article establishes several recognized, standard, inclusive, and scores of typical exact wave solutions to the MEW equation using the double G ' / G , 1 / G -expansion method. For specific parameter values, kink, periodic, periodic-singular, singular-kink, and other forms of solitons can be recovered from general solutions. The effect of the fractional parameter on wave forms has also been analyzed by depicting several graphs for different values of the fractional-order α. In order to illustrate the potential characteristics, three- and two-dimensional combined plots using Maple have been drawn. It has been established that the introduced approach is a potential tool for extracting new exact solutions to various nonlinear evolution equations (NLEEs) arising in engineering, science, and applied mathematics. [ABSTRACT FROM AUTHOR]

A lot of numerical formulations of physical phenomena contain 9 th -order BVPs. The presented probe intends to consider the spline solutions of the 9 th -order boundary value problems using Cubic B Spline(CBS). Ninth order boundary value problems arise in the study of laminar viscous flow in a semi-porous channel, astrophysics, hydrodynamic & hydro-magnetic stability. The derived technique is exceptionally useful and is appropriate for such kinds of linear and non-linear boundary value problems. Cubic B Spline(CBS) is successfully applied to mathematical models. The outcomes are contrasted to those presented in the literature, revealing that the introduced technique leads to an advisable estimation of the exact solution. [ABSTRACT FROM AUTHOR]

This research paper presents an in-depth investigation into the complex interactions governing stratified fluid flow in the presence of rotational and stretching phenomena, magnetic field influences, heat and mass transfer effects, and the incorporation of thermal and solutal-slips at fluid interfaces. Stratified fluid systems are commonly encountered in various natural and industrial processes, ranging from geophysical flows to chemical engineering applications, making a thorough understanding of these phenomena paramount. The study commences by formulating a comprehensive set of governing equations that account for the unique interplay of these multifaceted physical phenomena. Integrating thermal and solutal slip conditions at fluid interfaces introduces innovative prospects for precisely controlling and manipulating mass and heat transfer in these systems. This research paper extensively explores layered fluid dynamics, encompassing phenomena such as rotation and stretching, influences from magnetic fields, effects of heat and mass transfer, and the examination of thermal and solutal slip conditions. The insights obtained from this study not only enhance our comprehension of multi-physics fluid dynamics but also offer practical implications for streamlining processes across diverse fields. The principal findings and implications of this research can be summarized as follows: Various factors that affect fluid flow exhibit evident and discernible patterns. The mathematical model includes the Navier-Stokes equations with rotational and stretching terms, the Maxwell equations describing magnetic field effects, and the transport equations for heat and mass transfer. Additionally, thermal and solutal slip conditions at the fluid interfaces are incorporated to capture boundary layer dynamics. Numerical simulations are conducted to explore the intricate dynamics arising from this amalgamation of physical effects. The results reveal complex flow patterns, including stratification, boundary layer development, and vortical structures, offering insights into the behavior of fluids under the joint influence of rotational and stretching phenomena, magnetic fields, and thermal and solutal gradients. Furthermore, the impact of key parameters, such as rotation rate, stretching rate, magnetic field strength, and concentration gradients, is systematically analyzed to elucidate their effects on flow characteristics, heat and mass transfer rates, and concentration profiles within the stratified fluid layers. The Soret effect, or thermophoresis, causes nanoparticles to migrate away from hot regions due to fluid molecule flow and high energy levels. Elevating ξ N t results in decreased heat and mass transfer. The Prandtl number shows minimal influence on heat and mass transfer when increased. The disk separation, and fluid viscosity, significantly affect the rotational spectrum. As the rotational parameter increases, heat and mass transfer decrease. [ABSTRACT FROM AUTHOR]

• The power of computer modeling and simulation for advanced problem-solving is uncovered. • Preparedness is enhanced with insights into predicting the dynamics of virus-borne diseases. • Innovative solutions for preserving positivity in population dynamical problems are explored. The design of computer modelling has a vital role in the recent development of scientific literature. Creation, modification, analysis, and optimization of structures are uses of computer methods. The most significant benefit is communication through documentation, quality of design, designing electronic systems, and many more. According to the World Health Organization report, there are two types of transmission of Nipah virus infection, such as from animals to humans or humans to humans. More than 40% to 75% rate of death due to Nipah virus is estimated. The most infected regions are Thailand, the Philippines, Indonesia, and Cambodia. The susceptible (S), exposed (E), infected (I), and recovered (R) are compartments of the Nipah virus model. The bilinear incidence rates are considered during its modelling. Positivity, boundedness, equilibria, reproduction number, and stability results are part of the qualitative analysis of the model. After that, the design of the computer methods on the model predicts the efficiency, visualization, and results of the Nipah virus disease. The existing techniques, like Euler and Runge Kutta, could be more stable. They are highly time-dependent methods. But our proposed way, i.e., NSFD, is always positive, bounded, regular and consistent at any time step size. In conclusion, the nonstandard finite difference method (NSFD) restores a dynamical property such as positivity, boundedness, consistency, and stability. In the end, computing techniques are presented to support the qualitative analysis of the model. [ABSTRACT FROM AUTHOR]

The main purpose of the current study is to invetigate the influence of Brownian motion and thermophoresis diffusion in non-Newtonian Williamson fluid flow through exponentially stretching sheet with the effects of thermal radiation and the bioconvection of microorganisms. For this purpose, similarity functions are involved to transmute partial differential equations to corresponding ordinary differential equations. Then Runge–Kutta method with shooting technique is hired to evaluate the desired findings with utilization of MATLAB script. The fluid velocity becomes slow against strength of magnetic parameter and it boosts with mixed convection. The temperature rises with parameter of Brownian motion and thermophoresis. The bioconvection Lewis number diminishes the velocity field. Compared with the existing literature, the results show satisfactory congruence's. [ABSTRACT FROM AUTHOR]

In this study, the extended tanh-function method has been used to find further general travelling wave solutions for space-time fractional nonlinear partial differential equations, namely, the time fractional nonlinear Sine-Gordon equation and Klein–Gordon equation. The mentioned equations are useful for explaining a series of experimental seismic data, modelling of strain waves, and structures correlated to fault dynamics and the subduction slab, as well as slow earthquakes, episodic tremor, slow slip events, and tremor migration patterns. This method is used to attain exact solutions to a variety of nonlinear partial differential equations that were spatially temporal fractional. To get analytical solutions of the travelling wave type of certain nonlinear evolution equations, a power series in tanh was first utilized as an ansatz. These nonlinear fractional partial differential equations (NLFPDEs) are solved on a variety of non-rectangular domains. By using the fractional complex transform and the properties of the confirmable derivative, the two equations are reduced to ordinary differential equations. The solutions are sketched in 3D, and contour patterns, including king type, single soliton, double solitons, multiple solitons, bell shape, and other sorts of solutions. The achieved solutions are very much effective for explaining the above-stated phenomena. [ABSTRACT FROM AUTHOR]

Using illicit drugs has been on growth in all over the world especially in the USA, Europe and Asia. It is very harmful to society; it is the fourth foremost cause of death in the United States when taking overdose drug (about the same as motor vehicle crashes). A drug that has a significant detrimental effect on a population as a whole is heroin, above all illegal substances. This work discussesthenon-classical mathematical model of White and Comiskey, demonstrating heroin epidemics. We present the existence of stable equilibrium numerically & mathematically. We will apply two methods (i) Adams Bashforth PECE method and (ii) Grunwald-Letnikovmethod (GLM) and simulate the model using Matlab software package. [ABSTRACT FROM AUTHOR]

This research explores the complex and physical behavior, using four different theoretical methods, of water wave propagation with surface tension. A modern Benneye-Luke (BL) algorithm is used to identify a variety of unobtained distinct wave solution forms, such as multi-solitons, lumps and breath-solutions by modified Khater (MK) method, improved Riccati expansion (IRE) method, novel G ′ G expansion (NGE) method, and generalized Kudryashov (GK) method. The nature of the Hamiltonian method often discusses the properties of the model form. Furthermore, some of the solutions in various forms of plots can be clarified by the complex actions of water wave propagation. [ABSTRACT FROM AUTHOR]

Novel coronavirus disease is a burning issue all over the world. Spreading of the novel coronavirus having the characteristic of rapid transmission whenever the air molecules or the freely existed virus includes in the surrounding and therefore the spread of virus follows a stochastic process instead of deterministic. We assume a stochastic model to investigate the transmission dynamics of the novel coronavirus. To do this, we formulate the model according to the charectersitics of the corona virus disease and then prove the existence as well as the uniqueness of the global positive solution to show the well posed-ness and feasibility of the problem. Following the theory of dynamical systems as well as by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions of the extinction and the existence of stationary distribution. Finally, we carry out the large scale numerical simulations to demonstrate the verification of our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we present spherical antiferromagnetic Sν − magnetic electromotive conformable Φ τ , Φ ν , Φ β microscales in conformable deSitter space. Also, we get optical antiferromagnetic Sν − optimistic conformable Φ τ , Φ ν , Φ β densities. Finally, we obtain geometric antiferromagnetic Sν − magnetic conformable Φ τ , Φ ν , Φ β microscales in conformable deSitter space. • Spherical antiferromagnetic S ν -magnetic electromotive conformable microscales are proposed and analyzed. • Optical S ν -optimistic conformable density is constructed. • Microfluidic microscale is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the fractional compartmental model in the sense of Caputo derivative for the dynamics of the novel human papillomavirus, which causes cervical cancer. We study and investigate the dynamical analysis of a nonlinear fractional-order cervical cancer epidemic model with the nonstandard finite difference method. The newly proposed nonlinear fractional model is an extension of an integer-order cervical cancer mathematical model. We demonstrate the solution's existence, uniqueness, non-negativity, and boundedness by utilizing fundamental concepts of the fixed-point theory. The basic reproduction number, which analyzes whether or not the infection spreads to the population, is computed using the next-generation matrix method. We investigate the local and global asymptotic stability of the derived cervical-free and cervical-present equilibrium points and discuss the sensitivity of the basic reproduction number, which depends on the parameters of the proposed model. Furthermore, a mathematical simulation of the suggested continuous model is performed to evaluate the reported theoretical results using the nonstandard finite difference method. The acquired results are displayed, which show that a fractional parameter plays a pivotal role in controlling the cervical cancer. [ABSTRACT FROM AUTHOR]

We investigate numerical solutions of fractional-order Tricomi equation (LFTE) in fractal transonic flow media by employing the method of local fractional q-homotopy transform (LFq-HATM). This method is a combination of methods of homotopy analysis and q-Laplace transform. We express the solutions in terms of rapidly convergent power series where the basics functions are easily computable by Mathematica software. We present uniqueness and convergence analysis of the model via Banach's fixed point theory (BFPT). Reliability analysis of the numerical method is provided by figures and physical works. Obtained results indicate the strength and efficiency of the LEq-HATM. [ABSTRACT FROM AUTHOR]

Systems of high-dimensional nonlinear ordinary differential equations play a significant role in Physics and applied sciences including big-data optimization, financial models, epidemic disease models. In this paper, we are concerned with numerical solutions of Bao's system that is a 4-dimensional hyperchaotic system introduced by Bo-Cheng and Zhong (2008). We solve the Bao's system with both the Crank-Nicolson and power series methods. Crank-Nicolson method is eventually evolved into a new system whose solution is presented in a quite neat algorithmic manner. By adding standard Brownian motion to each term in the model, we express the Bao's system as a system of stochastic differential equations. We solve the stochastic system with an Euler-type approximate solution method. By adding noise and expressing time derivatives with Caputo-type fractional derivative, we study on synchronization and parameter estimation of the models. To the best of our knowledge, Bao's system has not been numerically solved with the methods employed in this paper previously, and this paper considers fractional and stochastic Bao's system for the first time in the history of research. Techniques employed by us in this paper may serve as a framework for solutions of many other systems of ordinary differential equations including Lorenz types and epidemic models. [ABSTRACT FROM AUTHOR]

Local fractional q-homotopy analysis transform method (q -HATM) is employed to solve the local fractional Helmholtz equation. Uniqueness and convergence analysis of the method is investigated by Banach's fixed point theory. Solutions are expressed in the form of rapidly series with fast computable basics by Mathematica software. Reliability analysis is provided. Computational results display that LFq-HATM is an efficient and powerful method to obtain solutions to the present equation and has the potential to be applicable to other related fractional-order systems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new SEIRS model and are concerned with stability and numerical solutions of the model. The model is generated under certain assumptions such as individuals are vaccinated or have a special treatment but do not carry lifelong immunity. After generating a new SEIRS model, we perturb the model into fractional time derivative form where Caputo type fractional-order derivative operators are employed. After showing existence and uniqueness of the non-negative solutions, we determine disease free steady-state point and basic reproduction number. We also determine endemic steady state points and study on stability of the fractional system in these equilibrium points. We solve fractional-order system approximately with an efficient Euler type numerical method. We conclude that the proposed system may serve as a kernel for understanding, analysis and computational solutions of a wide range of disease models in epidemiology. [ABSTRACT FROM AUTHOR]

In this article, an efficient local meshless technique is implemented for the numerical solution of an anomalous mobile-immobile solute transport process. The process is mathematically modeled as a time fractional mobile-immobile diffusion equation in sense of Caputo derivative. An implicit time integration procedure is used to semi-discretize the model in the time direction whereas the space derivatives of the model is discretized by the proposed meshless technique based on inverse multquadric radial basis function. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximate the solution on set of uniform and scattered nodes and it leads to a sparse and well-conditioned coefficient matrices. Numerical examinations on some test problems are performed to exhibit successful applications and accuracy of the local meshless technique on regular and irregular computational domains. [ABSTRACT FROM AUTHOR]

Fractional-stochastic quadratic-cubic nonlinear Schrödinger equation (QC-NLSE) describing propagation of solitons through optical fibers is analyzed. Hermite transforms, white noise analysis and an improved computational method are used to investigate uncertain solutions for QC-NLSE. Specifically, Hermite transformation is applied to convert fractional-stochastic differential equations by Wick-type into deterministic fractional differential equations with an integral term. Furthermore, inverse Hermite transformation is employed to obtain stochastic solutions in the white noise space. Characteristics of presented equations are shown by using some specific values of physical arguments on obtained solutions. [ABSTRACT FROM AUTHOR]

In this paper, the new series solutions of some fractional cancer tumor models are investigated by using residual power series method (RPSM). The RPSM is explained with Maclaurin expansion for the solution. One of the advantages of this method is quick and easy calculation to find series solutions by using mathematica software package. Graphical presentations for series solutions are given to explanation of the method. The obtained outcomes explain that process is applicable and reliable method to obtain numerical solutions of fractional equations. [ABSTRACT FROM AUTHOR]

This work employs two new modified computational schemes to find the exact travelling and solitary wave solutions of the general modified Degasperis-Procesi Camassa-Holm (DP CH) equation that is used to illustrate the dynamical behaviour of shallow water. These schemes are the modified exponential expansion and the modified Khater methods that are used to formulate the computational solutions in various formulas such as trigonometric, hyperbolic, exponential functions. The obtained solutions are explained and figured out their substantial contributions in three different types of sketches (three, two-dimensional, and contour plots). [ABSTRACT FROM AUTHOR]

We introduce the theory of optical spherical Heisenberg ferromagnetic spin of timelike spherical normal magnetic flows of particles by the spherical frame in de Sitter space. Also, the concept of timelike spherical normal magnetic particles is investigated, which may have evolution equations. Afterward, we reveal new relationships with some integrability conditions for timelike spherical normal magnetic flows in de-Sitter space. In addition, we obtain total phases for spherical normal magnetic flows. We also acquire perturbed solutions of the nonlinear Schrödinger's equation that governs the propagation of solitons in de-Sitter space S 1 2 . Finally, we provide some numerical simulations to supplement the analytical outcomes. [ABSTRACT FROM AUTHOR]

The basic aim of this research is to investigate the main features of the peristaltic flow of Johnson-Segalman fluid in a curved flow channel in the presence of a homogeneous-heterogeneous reaction. The fluid is considered electrically conducting with a radial magnetic field effect. The constitutive relation for energy is formulated with the addition of viscous dissipation and nonlinear thermal radiation. The slip and flexible wall boundary conditions are taken into consideration. The lubrication technique is used for the mathematical the modelling of the problem. The solution of the resulting nonlinear system of ODE's is computed numerically through NDSolve command of Mathematica, and graphical results are prepared for flow variables. It has been clearly noticed that flow is accelerated in the planer medium as compared to the curved channel, and the velocity of the fluid increases with a larger Weissenberg number. Moreover, the thermal profile has an inverse relation to the parameters, i.e., radiation, temperature ratio, and curvature. Furthermore, it is also observed that the magnitude of heat transfer coefficient rises significantly when a comparatively less curved channel is utilized, however, a reduction in concentration profile is witnessed in this case. Alternative impact of homogeneous and heterogeneous reactions on concentration profile are observed through graphical results. Application of the study include the usage of peristaltic pump in chemical industry and in pharmacology industry for the purpose of drug deliveries. [ABSTRACT FROM AUTHOR]

In this work, the time fractional Gardner equation is presented as a new fractional model for Atangana–Baleanu fractional derivative with Mittag-Leffler kernel. The approximate consequences are analysed by applying a recurrent process. The existence and uniqueness of solution for this system is discussed. To explain the effects of several parameters and variables on the movement, the approximate results are shown in graphics and tables. [ABSTRACT FROM AUTHOR]

The reaction-nonlinear diffusion model is analyze analytically, under both logistic and bistable growth regularization. These regularization techniques have been widely apply and employ in models of chemical phase separation. In this study, we mainly focus on construct the different wave structures are with the help of the generalized Riccati equation mapping method. This method is provided us the different hyperbolic, trigonometric, and rational solutions. These solutions help for the dynamic study of the reaction-nonlinear diffusion model. Moreover, for the physical significance, we construct the 3D and their corresponding contour by choosing the different values of the parameters. Additionally for the computational interests of the readers stability and consistency analysis were proved. • Analysis of the reaction-nonlinear diffusion model under logistic and bistable growth regularization. • Application of widely used regularization techniques in models of chemical phase separation. • Focus on constructing various wave structures using the generalized Riccati equation mapping method. • Construction of 3D and corresponding contour plots with varying parameter values for physical significance. • Presentation of stability and consistency analysis for computational interests of readers. [ABSTRACT FROM AUTHOR]

Propagation of the pressure waves in a liquid with gas bubbles is an important topic in the field of fluid dynamics and mathematical physics. The Kudryashov-Sinelshchikov equation is one of the models that describe the propagation of nonlinear waves in a bubbly liquid taking into consideration the viscosity of the liquid and the heat transfer. To explain such behaviors, we mainly focus in this study to explain the dynamics of localized waves and their variety of interaction solutions to a dimensionally reduced (2 + 1)-dimensional Kudryashov-Sinelshchikov equation with the aid of the Hirota bilinear method from N -soliton solutions. Four different forms of localized waves, including solitons, lumps, breathers, and rogues, are derived from the aforesaid equation based on the long wave limit approach. In particular, the localized waves can be used to find interaction solutions, which are the single breather or single lump formed by two solitons; interaction between one line soliton and one breather, as well as one line soliton and one lump soliton among the three solitons; interaction of the two-line soliton and one periodic breather, two periodic breathers, periodic breather and one lump soliton from the four solitons. The direction of propagation, phase shifts, shape, energy, and the variety of interaction solutions of localized waves are affected by these parameters. Moreover, analytical and graphical illustrations of these interaction solutions and their propagation properties are shown by the three-dimensional and density plots with the help of Maple 17. These newly discovered solutions in this study can be used to illustrate the interaction phenomenon of localized waves on ocean surfaces. [ABSTRACT FROM AUTHOR]

This article uses a fractional approach to investigate the system of tsunami wave propagation along an oceanic coastline. The tsunami wave system is considered under singular and nonsingular fractional operators. The double Laplace transform (LT) with Adomian decomposition method (ADM) is implemented to analyse this model. Some theoretical features of the considered fractional tsunami systems are explored via fixed point notions. Based on the shallow-water hypothesis, the current model has been explored. It is shown that changes in sea depth and coast slope have an impact on the tsunami wave's speed and amplification at various time scales. From the numerical simulations it is observed that decrease in the fractional order decreases the tsunami wave velocity as well as height. [ABSTRACT FROM AUTHOR]

In this work, we apply three different techniques to solve the Fitzhugh–Nagumo equation that is an important equation used to describe the propagation of electrical signals in excitable media, such as nerve fibers. Residual power series method (RPSM), homotopy perturbation method (HPM), and a modified fractional Taylor expansion, are applied to this nonlinear equation to obtain approximate solutions. By comparing the exact solution with the approximate solutions obtained from the methods suggested we demonstrate that these methods are efficient tools to solve nonlinear fractional partial differential equations (NFPDE) this is due to the high accuracy obtained. To support the current solution investigation, various graphs in 2D and 3D are shown. • Three different techniques are applied to solve the Fitzhugh–Nagumo equation. • By comparing the exact solution with the approximate solutions obtained from the methods. • To support the current solution investigation, various graphs in 2D and 3D are shown. [ABSTRACT FROM AUTHOR]

In this digital, internet-based world, it is not new to face cyber attacks from time to time. A number of heavy viruses have been made by hackers, and they have successfully given big losses to our systems. In the family of these viruses, the Stuxnet virus is a well-known name. Stuxnet is a very dangerous virus that probably targets the control systems of our industry. The main source of this virus can be an infected USB drive or flash drive. In this research paper, we study a mathematical model to define the dynamical structure or the effects of the Stuxnet virus on our computer systems. To study the given dynamics, we use a modified version of the Caputo-type fractional derivative, which can be used as an old Caputo derivative by fixing some slight changes, which is an advantage of this study. We demonstrate that the given fractional Caputo-type dynamical model has a unique solution using fixed point theory. We derive the solution of the proposed non-linear non-classical model with the application of a recent version of the Predictor–Corrector scheme. We analyze various graphs at different values of the arrival rate of new computers, damage rate, virus transmission rate, and natural removal rate. In the graphical interpretations, we verify the values of fractional orders and simulate 2-D and 3-D graphics to understand the dynamics clearly. The major novelty of this study is that we formulate the optimal control problem and its important consequences both theoretically and mathematically, which can be further extended graphically. The main contribution of this research work is to provide some novel results on the Stuxnet virus dynamics and explore the uses of fractional derivatives in computer science. The given methodology is effective, fully novel, and very easy to understand. [ABSTRACT FROM AUTHOR]

In this study, our focus is on the construction of novel soliton solutions of non-linear Schrödinger equation with parabolic law and non-local law non-linearities via new extended hyperbolic function method. The acquired solutions are original and could be helpful in the field of nonlinear optics, fluid dynamics, and plasma physics. From these outcomes, it is believed that this method is a promising technique to handle a wide variety of such type of equations. For physical understanding and better realization of our constructed solutions, some of the obtained solutions under appropriate parameters are demonstrated by 2D and 3D plots. Analysis discloses that the proposed scheme is consistent and can be applied to more advanced models in engineering and physics. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to introduce symmetry analysis and Nucci's reduction method for revealing the exact solutions of the periodic Hunter–Suxon equation, which is parameterized by the speed of the Galilean frame. Under one-point similarity transformations, we obtained a set of generators that transformed the given equation into an ordinary differential equation, which can be conveniently taken into consideration for exact solutions. Under special choices, we got three separate families of vector fields out of the problem and constructed solutions for every family. In each case, the Nucci reduction technique generated a solution with a first integral. 3D, density, and contour graphics are given for a better understanding of the solutions. [ABSTRACT FROM AUTHOR]

In this study, we construct the abundant families of soliton solutions for the generalized (2+1)-dimensional Camassa–Holm–KP equation. This equation is used in tiny amplitude shallow water waves. The solutions are obtained in the form of Jacobi elliptic function solutions which are the soliton and solitary wave solutions. They are observed in the form of shock, bright, combined complex shock, singular and periodic waves, as well as rational solutions. Some techniques are applied to obtain the solutions with the help of Mathematica namely as; ϕ 6 -model expansion and a new modified extended direct algebraic method. In nonlinear dynamics, the acquired results are particularly helpful for studying and confirming the analytical solutions with numerical and experimental work. Additionally, the contour diagrams and three- and two-dimensional representations of the solutions are drawn for the various parameter values. [ABSTRACT FROM AUTHOR]

In this study, a general second-order evolution equation of the Fisher-type, with time-dependent variable coefficients, is considered. This equation contains many well-known equations, and obtained results may be applicable in investigating other evolution equations. Lie symmetries and corresponding invariant solutions of the considered problem are studied by a non-traditional Lie symmetry method (LSM). Prolongation of the model is an essential part of the Lie symmetry method, which in the current work, we analyze by the heir-equations. Finally, different types of solutions depending on the variable coefficients, such as the exponential solutions, trigonometric solutions, Bessel solutions, and Mathieu solutions, are extracted. [ABSTRACT FROM AUTHOR]

In this article, the stochastic Phi-4 model is under consideration analytically. The stochastic Phi-4 equation has been crucial to nuclear and particle physics. The randomness of the nuclear particle at the micro level is represented by the stochastic phenomena which are shown by the white noise. The stochastic version of the Phi-4 model is investigated for the first time analytically to gain the soliton solutions by using the two techniques such as Sardar sub-equation and modified exponential rational function. The stochastic soliton solutions are successfully constructed in the form of exponential, trigonometric, and hyperbolic forms. Additionally, the stability analysis of this model is observed. Lastly, the stochastic behavior of some solutions is shown in the form of 2D, and 3D by choosing the different values of parameters. [ABSTRACT FROM AUTHOR]

In this article, a nonlinear dispersive structure namely the modified Benjamin–Bona–Mahony (BBM) model is studied by employing three different approaches to develop some new analytical and semi-analytical solutions. The modified extended t a n hyperbolic function method, the improved F -expansion method and the Adomian decomposition method are implemented to obtain various interesting wave structures. The comparison among various types of solutions is analyzed to study the corresponding absolute error. Furthermore, the stability of the results along with the modulation instability are successfully deliberated. The 3D, contour and 2D graphs are visualized for several fascinating exact solutions to comprehend their behavior. [ABSTRACT FROM AUTHOR]