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Our paper proposes a system of nonlinear mixed variational inequality problems (SNMVIPs) on Banach spaces. Under suitable assumptions, using the K-Fan fixed point theorem and Minty techniques, we demonstrate that the solution set to the SNMVIP is nonempty, weakly compact, and unique. Additionally, we suggest a stability result for the SNMVIPs by perturbing the duality mappings. Furthermore, we present an optimal control problem that is governed by the SNMVIPs and show that it can be solved. [ABSTRACT FROM AUTHOR]

In this paper, we study left-invariant cross curvature solitons on Lorentzian three-dimensional Lie groups and classify these solitons. [ABSTRACT FROM AUTHOR]

This article introduces a new iterative transform method and homotopy perturbation transform method along with a natural transform to analyze the multi-dimensional Navier-Stokes equations. To solve the fractional-derivative, the Caputo-Fabrizio definition of the fractional derivative was employed. Four examples were considered to examine the efficacy and accuracy of the proposed methods. The efficiency and accuracy were also demonstrated by the solution comparison via graphs. The proposed methods' convergence and uniqueness are also discussed. The methods mentioned above are straightforward and support a high rate of convergence. [ABSTRACT FROM AUTHOR]

This note introduces a new class of preinvexity called (h 1 , h 2) -Godunova-Levin preinvex functions that generalize earlier findings. Based on these notions, we developed Hermite-Hadamard, weighted Fejér, and trapezium type inequalities. Furthermore, we constructed some non-trivial examples in order to verify all the developed results. In addition, we discussed some applications related to the trapezoidal formula, probability density functions, special functions and special means. Lastly, we discussed the importance of order relations and left two open problems for future research. As an additional benefit, we believe that the present work can provide a strong catalyst for enhancing similar existing literature. [ABSTRACT FROM AUTHOR]

In this article, a Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model is considered. The equilibrium analysis and reproduction number are studied. The conventional models have made assumptions of homogeneity in disease transmission that contradict the actual reality. However, it is crucial to consider the heterogeneity of the transmission rate when modeling disease dynamics. Describing the heterogeneity of disease transmission mathematically can be achieved by incorporating fuzzy theory. A numerical scheme nonstandard, finite difference (NSFD) approach is developed for the studied model and the results of numerical simulations are presented. Simulations of the constructed scheme are presented. The positivity, convergence and consistency of the developed technique are investigated using mathematical induction, Jacobean matrix and Taylor series expansions respectively. The suggested scheme preserves all these essential characteristics of the disease dynamical models. The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease. Moreover, the obtained method generates plausible predictions that can be used by regulators to support the decision-making process to design and develop control strategies. Effects of the natural immunity on the infected class are studied which reveals that an increase in natural immunity can decrease the infection and vice versa. [ABSTRACT FROM AUTHOR]

In the present paper we study Ricci pseudo-symmetry, Z-Ricci pseudo-symmetry and concircularly pseudo-symmetry conditions on a mixed generalized quasi-Einstein spacetime MG(QE)4. Also, it is proven that if d ≠ Λ, then MG(QE)4 spacetime does not admit heat flux, where d and Λ are the function and the cosmological constant, respectively. In the end of this paper we construct a non-trivial example of MG(QE)4 to prove its existence. [ABSTRACT FROM AUTHOR]

The existence of a positive solution to a system of nonlinear semipositone Hadamard fractional BVP with the p-Laplacian operator is examined in this research. The boundary value problem's associated Green's function and some of its properties are first obtained. Additionally, the existence results are established using the nonlinear alternative of the Leray–Schauder theorem and the Guo–Krasnosel'skii fixed-point theorem. [ABSTRACT FROM AUTHOR]

The novel coronavirus disease (SARS-CoV-2) has caused many infections and deaths throughout the world; the spread of the coronavirus pandemic is still ongoing and continues to affect healthcare systems and economies of countries worldwide. Mathematical models are used in many applications for infectious diseases, including forecasting outbreaks and designing containment strategies. In this paper, we study two types of SIR and SEIR models for the coronavirus. This study focuses on the discrete-time and fractional-order of these models; we study the stability of the fixed points and orbits using the Jacobian matrix and the eigenvalues and eigenvectors of each case; moreover, we estimate the parameters of the two systems in fractional order. We present a statistical study of the coronavirus model in two countries: Saudi Arabia, which has successfully recovered from the SARS-CoV-2 pandemic, and China, where the number of infections remains significantly high. [ABSTRACT FROM AUTHOR]

In the present paper, we characterize m-dimensional ζ -conformally flat L P -Kenmotsu manifolds (briefly, (L P K) m ) equipped with the Ricci–Yamabe solitons (RYS) and gradient Ricci–Yamabe solitons (GRYS). It is proven that the scalar curvature r of an (L P K) m admitting an RYS satisfies the Poisson equation Δ r = 4 (m − 1) δ { β (m − 1) + ρ } + 2 (m − 3) r − 4 m (m − 1) (m − 2) , where ρ , δ (≠ 0) ∈ R . In this sequel, the condition for which the scalar curvature of an (L P K) m admitting an RYS holds the Laplace equation is established. We also give an affirmative answer for the existence of a GRYS on an (L P K) m . Finally, a non-trivial example of an L P -Kenmotsu manifold (L P K) of dimension four is constructed to verify some of our results. [ABSTRACT FROM AUTHOR]