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The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings ( F - N - V - M s ), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard ( H ⋅ H ) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes. [ABSTRACT FROM AUTHOR]

The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical model to capture the transmission dynamics of MERS-CoV. We incorporate some novel parameters related to birth and mortality rates, which are essential factors influencing the spread of the virus. We obtain epidemiological data from reliable sources to estimate the model parameters. We compute its basic reproduction number (R0). Stability theory is employed to analyze the local and global properties of the model, providing insights into the system's equilibrium states and their stability. Sensitivity analysis is conducted to identify the most critical parameter affecting the transmission dynamics. Our findings revealed important insights into the transmission dynamics of MERS-CoV. The stability analysis demonstrated the existence of stable equilibrium points, indicating the long-term behavior of the epidemic. Through the evaluation of optimal control strategies, we identify effective intervention measures to mitigate the spread of MERS-CoV. Our simulations demonstrate the impact of time-dependent control variables, such as supportive care and treatment, in reducing the number of infected individuals and controlling the epidemic. The model can serve as a valuable tool for public health authorities in designing effective control and prevention strategies, ultimately reducing the burden of MERS-CoV on global health. [ABSTRACT FROM AUTHOR]

The symmetric function class interacts heavily with other types of functions. One of these is the convex function class, which is strongly related to symmetry theory. In this study, we define a novel class of convex mappings on planes using a fuzzy inclusion relation, known as coordinated up and down convex fuzzy-number-valued mapping. Several new definitions are introduced by placing some moderate restrictions on the notion of coordinated up and down convex fuzzy-number-valued mapping. Other uncommon examples are also described using these definitions, which can be viewed as applications of the new outcomes. Moreover, Hermite–Hadamard–Fejér inequalities are acquired via fuzzy double Aumann integrals, and the validation of these outcomes is discussed with the help of nontrivial examples and suitable choices of coordinated up and down convex fuzzy-number-valued mappings. [ABSTRACT FROM AUTHOR]

The concept of convexity is fundamental in order to produce various types of inequalities. Thus, convexity and integral inequality are closely related. The objectives of this paper are to present a new class of up and down convex fuzzy number valued functions known as up and down exponential trigonometric convex fuzzy number valued mappings ( U D E T - convex FNVMs) and, with the help of this newly defined class, Hermite–Hadamard-type inequalities (H–H-type inequalities) via fuzzy inclusion relation and fuzzy fractional integral operators having exponential kernels. This fuzzy inclusion relation is level-wise defined by the interval-based inclusion relation. Furthermore, we have shown that our findings apply to a significant class of both novel and well-known inequalities for U D E T - convex   F N V M s. The application of the theory developed in this study is illustrated with useful instances. Some very interesting examples are provided to discuss the validation of our main results. These results and other approaches may open up new avenues for modeling, interval-valued functions, and fuzzy optimization problems. [ABSTRACT FROM AUTHOR]

This article studies a biological population model in the context of a fractional Caputo-Fabrizio operator using double Laplace transform combined with the Adomian method. The conditions for the existence and uniqueness of solution of the problem under consideration is established with the use of the Banach principle and some theorems from fixed point theory. Furthermore, the convergence analysis is presented. For the accuracy and validation of the technique, some applications are presented. The numerical simulations present the obtained approximate solutions with a variety of fractional orders. From the numerical simulations, it is observed that when the fractional order is large, then the population density is also large; on the other hand, population density decreases with the decrease in the fractional order. The obtained results reveal that the considered technique is suitable and highly accurate in terms of the cost of computing, and can be used to analyze a wide range of complex non-linear fractional differential equations. [ABSTRACT FROM AUTHOR]

The current manuscript investigates the exact solutions of the modified Benjamin-Bona-Mahony (BBM) equation. Due to its efficiency and simplicity, the modified auxiliary equation method is adopted to solve the problem under consideration. As a result, a variety of the exact wave solutions of the modified BBM equation are obtained. Furthermore, the findings of the current study remain strong since Jacobi function solutions generate hyperbolic function solutions and trigonometric function solutions, as liming cases of interest. Some of the obtained solutions are illustrated graphically using appropriate values for the parameters. [ABSTRACT FROM AUTHOR]

In this paper, we propose two scaled Dai–Yuan (DY) directions for solving constrained monotone nonlinear systems. The proposed directions satisfy the sufficient descent condition independent of the line search strategy. We also reasonably proposed two different relations for computing the scaling parameter at every iteration. The first relation is proposed by approaching the quasi-Newton direction, and the second one is by taking the advantage of the popular Barzilai–Borwein strategy. Moreover, we propose a robust projection-based algorithm for solving constrained monotone nonlinear equations with applications in signal restoration problems and reconstructing the blurred images. The global convergence of this algorithm is also provided, using some mild assumptions. Finally, a comprehensive numerical comparison with the relevant algorithms shows that the proposed algorithm is efficient. [ABSTRACT FROM AUTHOR]

In the present study, we explore the time-dependent convectional flow of a rheological nanofluid over a turning cone with the consolidated impacts of warmth and mass exchange. It has been shown that if the angular velocity at the free stream and the cone's angular velocity differ inversely as a linear time function, a self-similar solution can be obtained. By applying sufficient approximation to the boundary layer, the managed conditions of movement, temperature, and nanoparticles are improved; afterward, the framework is changed to a non-dimensional framework utilizing proper comparability changes. A numerical solution for the obtained system of governing equations is achieved. The effect of different parameters on the velocity, temperature, and concentration profiles are discussed. Tangential velocity is observed to decrease with an increase in the Deborah number, whereas tangential velocity increases with increasing values of the angular velocity ratio, relaxation to the retardation time ratio, and buoyancy parameter. Expansion in the Prandtl number is noted to decrease the boundary layer temperature and thickness. The temperature is seen to decrease with an expansion in the parameters of lightness, thermophoresis parameter, and Brownian movement. It is discovered that the Nusselt number expands by expanding the lightness parameter and Prandtl number, whereas it increases by decreasing the Deborah number. We also noticed that the Sherwood number falls incrementally in Deborah and Prandtl numbers, but it upsurges with an increase in the buoyancy parameter. [ABSTRACT FROM AUTHOR]

In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Mart i ´ nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the time-fractional two-mode coupled Burgers equation with the Caputo fractional derivative. A modified homotopy perturbation method coupled with Laplace transform (He-Laplace method) is applied to find its approximate analytical solution. The method is to decompose the equation into a series of linear equations, which can be effectively and easily solved by the Laplace transform. The solution process is illustrated step by step, and the results show that the present method is extremely powerful for fractional differential equations. [ABSTRACT FROM AUTHOR]

In the present work, the propagation of (non)linear electrostatic waves is reported in a normal (electron–ion) magnetoplasma. The inertialess electrons follow a non-extensive q-distribution, while the positive inertial ions are assumed to be warm mobile. In the linear regime, the dispersion relation for both the fast and slow modes is derived, whose properties are analyzed parametrically, focusing on the effect of nonextensive parameter, component of parallel anisotropic ion pressure, component of perpendicular anisotropic ion pressure, and magnetic field strength. The reductive perturbation technique is employed for reducing the fluid equation of the present plasma model to a Zakharov–Kuznetsov (ZK) equation. The parametric role of physical parameters on the characteristics of the symmetry planar structures such solitary waves is investigated. Furthermore, the stability of the pulse soliton solution of the ZK equation against the oblique perturbations is investigated. Furthermore, the dependence of the instability growth rate on the related physical parameters is examined. The present investigation could be useful in space and astrophysical plasma systems. [ABSTRACT FROM AUTHOR]