Journal of Mathematical Modeling
Volume:11 Issue: 3, Summer 2023

The main purpose of this study is to construct a new approach for solving a constrained matrix game where the payoffs and the constraints are LR-fuzzy numbers. The method that we propose here is based on chance constraints and on the concept of a comparison of fuzzy numbers. First, we formulate the fuzzy constraints of each player as chance constraints with respect to the possibility measure. According to a ranking function $\mathcal{R}$, a crisp constrained matrix game is obtained. Then, we introduce the concept of $\mathcal{R}$-saddle point equilibrium. Using results on ordering fuzzy numbers, sufficient existence conditions of this concept are provided. The problem of computing this solution is reduced to a  pair of primal-dual linear programs. To illustrate the proposed method, an example of the market competition game is given.

Machine learning (ML) techniques have become a point of interest in medical research. To predict the existence of a specified disease, two methods K-Nearest Neighbors (KNN) and logistic regression can be used, which are based on distance and probability, respectively. These methods have their problems, which leads us to use the ideas of both methods to improve the prediction of disease outcomes. For this sake, first, the data is transformed into another space based on logistic regression. Next, the features are weighted according to their importance in this space. Then, we introduce a new distance function to predict disease outcomes based on the neighborhood radius. Lastly, to decrease the CPU time, we present a partitioning criterion for the data.

This paper deals with a stochastic delay Gompertz model under regime switching with Levy jumps. Firstly, the existence of a unique global positive solution has been derived. Secondly, sufficient conditions for extinction and persistence in mean are obtained. Finally, an example is given to illustrate our main results.The results in this paper indicate that Levy jumps noise, the white noise and switching noise have certain effects on the properties of the model.

This paper aims to present a new and efficient numerical method to approximate the solution of the fractional model of human T-cell lymphotropic virus I (HTLV-I) infection $CD4^+T$-cells. The approximate solution of the model is obtained using the shifted Chebyshev collocation spectral method. This model relates to the class of nonlinear ordinary differential equations. The proposed algorithm reduces the Caputo sense fractional model to a system of nonlinear algebraic equations that can be solved numerically. The convergence of the proposed method is investigated. The graphical result is compared with existing numerical methods reported in the literature to indicate the efficiency and reliability of the presented method.

The aim of the current paper is to study a partially described inverse eigenvalue problem of  a specific symmetric  matrix, and prove some properties of such matrix. The problem includes the construction of the matrix by  the  minimal eigenvalue of all  leading principal submatrices  and eigenpair $(\lambda_2^{(n)},x)$ such that $ \lambda_2^{(n)}$ is the maximal eigenvalue of the required matrix. We investigate  conditions for the solvability of the problem, and finally an algorithm and  its numerical results are presented.

Let $I\subseteq\mathbb{R}$ be an interval and $\beta\colon I\to I$ a strictly increasing continuous function with a unique fixed point $s_0\in I$ satisfying $(t-s_0)(\beta(t)-t)\le 0$ for all $t\in I$. Hamza et al. introduced the general quantum difference operator $D_{\beta}$ by $D_{\beta}f(t):=\frac{f(\beta(t))-f(t)}{\beta(t)-t}$ if $t\ne s_0$ and $D_{\beta}f(t):=f'(s_0)$ if $t=s_0$.   In this paper, we establish results concerning Taylor's formula associated with $D_{\beta}$. For this, we define two types of monomials and then present our main results. The obtained results are new in the literature and are useful for further research in the field.

This paper proposes two effective nonmonotone trust-region frameworks for solving nonlinear unconstrained optimization problems while provide a new effective policy to update the trust-region radius. Conventional nonmonotone trust-region algorithms apply a specific nonmonotone ratio to accept  new trial step and update the trust-region radius. This paper recommends using the nonmonotone ratio only as an acceptance criterion for a new trial step. In contrast, the monotone ratio or a hybrid of monotone and nonmonotone ratios is proposed as a criterion for updating the trust-region radius. We investigate the global convergence to first- and second-order stationary points for the proposed approaches under certain classical assumptions.  Initial numerical results indicate that the proposed methods significantly enhance the performance of nonmonotone trust-region methods.

This article investigates a fractional-order predator-prey model incorporating prey refuge and anti-predator behaviour on predator species. For our proposed model, we prove the existence, uniqueness, non-negativity and boundedness of solutions. Further, all biologically possible equilibrium points and their stability analysis for the proposed system are carried out with the linearization process. Moreover, by using an appropriate Lyapunov function, the global stability of the co-existence equilibrium point is studied. Finally, we provide numerical simulations to demonstrate how the theoretical approach  is  consistent.

In this work, a Semi-Algebraic Mode Analysis (SAMA) technique for multigrid waveform relaxation method applied to the finite element discretization on rectangular and regular triangular grids in two dimensions and cubic and triangular prism elements in three dimensions for the heat equation is proposed.  For all the studied cases especially for the general triangular prism element, both the stiffness and mass stencils are introduced comprehensively. Moreover, several numerical examples are included to illustrate the efficiency of the convergence estimates. Studying this analysis for the finite element method is more involved and more general than that finite-difference discretization since the mass matrix must be considered. The proposed analysis results are a very useful tool to study the behavior of the multigrid waveform relaxation method depending on the parameters of the problem.

In present work, we discuss local existance and uniqueness of solution to the $\psi-$Hilfer fractional differential problem. By using the Picard successive approximations, we construct a computable iterative scheme uniformly approximating solution. Two illustrative examples are given to support our findings.

In this paper, we use the CAS wavelets as basis functions to numerically solve a system of nonlinear Fredholm integro-differential equations. To simplify the problem, we transform the system into a system of algebraic equations using the collocation method and operational matrices. We show the convergence of the presented method and then demonstrate its high accuracy with several illustrative examples. This approach is particularly effective for equations that admit periodic functions because the employed basis CAS functions are inherently periodic. Throughout our numerical examples, we observe that this method provides exact solutions for equations with trigonometric functions at a lower computational cost when compared to other methods.

In this paper, a new synchronization criterion for leader-follower fractional-order chaotic systems using partial contraction theory under an undirected fixed graph is presented. Without analyzing the stability of the error system, first the condition of partial contraction theory for the synchronization of fractional systems is explained, and then the input control vector is designed to apply the condition. An important feature of this control method is the rapid convergence of all agents into a common state. Finally, numerical examples with corresponding simulations are presented to demonstrate the efficiency and performance of the stated method in controlling fractional-order systems. The simulation results show the appropriate design of the proposed control input.