International Journal of Neutrosophic Science

Finite-time stability is a critical property for systems where rapid stabilization is required, as it ensures that the system reaches and maintains equilibrium within a specified time frame, regardless of initial conditions. This contrasts with asymptotic stability, which only guarantees eventual convergence over an indefinite period. This research focuses on demonstrating the finite-time stability of the glycolysis reaction-diffusion system at its equilibrium point. The equilibrium points of the system are derived, and finite-time stability conditions are established. Definitions and lemmas are provided to support the theoretical framework, including conditions for finite-time convergence and Lyapunov stability. A key result shows that the system possesses a unique equilibrium point that can achieve finite-time stability under certain conditions. Additionally, the finite-time synchronization scheme is discussed, highlighting the process of rapidly achieving synchronized behavior in reaction-diffusion systems. The proposed method involves associating the main system with a response system and addressing synchronization discrepancies through the introduction of an error vector. This research provides a robust framework for understanding and achieving finite-time stability and synchronization in complex reaction-diffusion systems.

The utilization of neutrosophic fuzzy logic with machine learning constitutes a revolutionary way of improving epidemic modelling. With the help of Weka, this method solves the problem of uncertainty and vagueness that is characteristic of epidemic processes with the help of neutrosophic equations. These equations enhance the way how indeterminacy of epidemic levels can be modelled, therefore enhancing predictions of complex networks. The effectiveness of the proposed framework is confirmed by extensive evaluations providing extensive tables and visualizations regarding the improvements in the accuracy and reliability of the models. Further, the work explores time-optimal control strategies of SIR epidemic models. It shows exactly how bang-bang controls work avoiding the duration of outbreaks drastically, especially if introduced with delayed interventions. This finding is especially important for controlling the health of livestock since the response to disease outbreaks has to be done as soon as possible because of stringent measures on animal health. Altogether, the analysis presented therein contains strong recommendations that would help to improve the handling of epidemics and better understand the approaches to employ in decision-making under conditions of risk and ambiguity.

The fuzzy stock administration demonstrates displayed in this work employments neutrosophic set hypothesis, pentagonal fuzzy numbers, and the Graded mean Integration Representation (GMIR) strategy for defuzzification. Request rates, arrange amounts, utilization rates, holding costs, setup costs, and deficiency costs are all spoken to as fuzzy parameters within the demonstrate to account for the inborn instability and vacillation. To reduce by and large costs, the whole cost work is calculated, taking setup, holding, and shortage costs into consideration. In arrange to speak to the combined impacts of a few fetched components, the overall taken a toll work is rearranged and the ideal arrange amount is built up beneath fuzzy conditions utilizing pentagonal fuzzy parameters. The demonstrate is assessed beneath different degrees of instability through a case-based investigation, advertising an exhaustive system for making choices on stock administration in equivocal and dubious circumstances. The results appear how versatile and capable the show is for improving fetched advancement and stock control.

The Neutrosophic Cordial Labeling Graph integrates both neutrosophic labeling and Cordial Labeling. Building on our previous work, we have extended our study to include Neutrosophic Cordial Labeling for Helm and Closed Helm Graphs. This extension allows us to explore the application of Neutrosophic Cordial Labeling in more complex graph structures, providing insights into their properties and relationships. One of the key aspects of our research is investigating the relationship between Cordial and Neutrosophic Cordial Labeling. By comparing and contrasting these labeling techniques [4], we aim to uncover similarities, differences, and potential synergies between them. This analysis contributes to a deeper understanding of graph labeling methodologies and their implications in various graph-theoretic applications [18]. Our research contributes to the advancement of graph labeling theory, particularly in the context of Neutrosophic Cordial Labeling and its applications in Helm and Closed Helm Graphs. By exploring these concepts and relationships, we aim to enhance the theoretical foundation and practical utility of graph labeling techniques in diverse domains [16,17].

In this work, we present and analyze new probability distribution by generalizing the classical Maxwell–Boltzmann model to neutrosophic structure. The generalized structure, known as the neutrosophic Maxwell (NMX) model that is designed to analyze data with imprecise or vague information. Closed-form expressions for cumulative distribution functions, probability density functions, survival functions, hazard functions, and moments, moment generating functions, mode, skewness, and kurtosis are derived as part of its detailed mathematical and statistical characteristics. The parameter estimation of the suggested model is carried out employing the maximum likelihood estimation (MLE) technique, and the statistical properties of the estimators are discussed in uncertain environments. The inverse cumulative distribution method is established to generate random samples from the proposed model and to evaluate the efficiency of the MLE method. Eventually, a real-world healthcare data set is used to show the efficacy of the proposed model.  This research provides new knowledge in the field of neutrosophic statistics, laying a foundation for further exploration in this area

The study defines a neutrosophic N-subalgebra and a level set of a neutrosophic N-structure on Sheffer stroke UP-algebras. It appears that these concepts are integral to understanding the behavior of neutrosophic logic within the framework of Sheffer stroke UP-algebras. The study establishes a relationship between subalgebras and level sets on Sheffer stroke UP-algebras. Specifically, it proves that the level set of neutrosophic Nsubalgebras on this algebra is its subalgebra, and vice versa. This indicates a tight connection between these concepts within the given algebraic structure. It is stated that the family of all neutrosophic N-subalgebras of a Sheffer stroke UP-algebra forms a complete distributive lattice. This suggests that there is a well-defined structure and order among these subalgebras, allowing for systematic analysis. The study describes a neutrosophic N-ideal of a Sheffer stroke UP-algebra and provides some of its properties. Additionally, it is shown that every neutrosophic N-ideal of a Sheffer stroke UP-algebra is also its neutrosophic N-subalgebra, though the inverse is generally not true. This highlights the specific characteristics and behavior of neutrosophic Nideals within the given algebraic context.

In this paper, we employ the classical topological preorder to introduce the concept of topologically bounded sets, in order to relate it to the Collatz conjecture problem. In addition, this preorder allows us to derive some results about topologically convex sets, showing that these form a convex structure. Finally, using this topological preorder, we define the neutrosophic continuous sets and establish the necessary conditions to identify the points that are connected to these sets, which form a topological convex set.

In this paper, we present new concept namely neutrosophic algebra. Some types of notions such as KU-module, KU-ideal and KU-submodule. We proved that if AI is minimal submodule, then AI ascending (descending) chain condition. On the other hand, more results about Neutrosophic exact sequence and Neutrosophic homomorphism KU-module have been presented.

This research proposes a novel approach to rank the problems faced by female employees in various sectors by utilizing the concept of the bipolar single-valued Neutrosophic soft set-in variable. The feature assessment used an enormous collection of multi-observer information as a basis for examining the issues encountered by women employed in a variety of sectors. An effective method for identifying the Neutrosophic domain's choice-making problem is the Neutrosophic Soft Set. The creation of similar tables has shaped the investigation into classification. In a Neutrosophic setting, grouping objects and persons according to their properties, capacities, the result, etc., is advantageous.

This paper introduces a new class of mappings termed (α̂,β̂)−Ω-contraction mapping (briefly, "(α̂,β̂)−Ω−CMap") and establishes certain fixed-point (FP) results in the framework of Algebra fuzzy metric space. Additionally, we expanded our results to include the existence of a nonlinear integral equation solution. Results from this study improve, expand and generalization certain previously published results in the literature.

This paper is devoted to introducing a novel numerical approach for approximating solutions to Boundary Value Problems (BVPs). Such an approach will be carried out by using a new version of the shooting method, which would convert the BVP into a linear system of two initial value problems. This system can then be solved by the so-called Obreschkoff approach. The numerical solution of the main BVP will ultimately be a linear combination of the solutions of the two system of equations. Two physical applications will be presented in order to confirm that the suggested numerical technique is valid.

Over the past few decades, the traditional critical path method and its various generalizations have become the most popular technique for managing complex projects. It plays a crucial role in differentiating between critical and non-critical tasks to enhance project schedules. For the first time in the literature, our proposed model implements two algorithms for the study of the critical path method, each addressing an advanced framework in the form of a single-valued triangular neutrosophic. The proposed algorithm 1 utilizes Python to extended Dijkstra’s algorithm under the neutrosophic framework, while the proposed algorithm 2 employs linear programming for optimality checks, which is solved using LINGO. Our comparison with previous research on the critical path method shows that the proposed algorithms are better at dealing with uncertainty, making project schedules more reliable and flexible. The findings lead to the proposed algorithm framework, combined with Python and LINGO, to enhance decision-making and improve the accuracy and efficiency of critical path identification in complex project environments.

This study, aims to consider the coefficients of the reciprocal Gamma function in order introduce a linear operator by the means of Hadamard product. Thus, we define a new subclass of uniformly starlike functions of order 𝛼, Γ−1(𝛼). Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions 𝑓∈Γ−1(𝛼). In addition, we investigate the inclusion conditions for the Hadamard product and the Integral transform.

This paper deals with some inverse problems for nonlinear time-dependent PDEs in one spatial dimension, we investigate an inverse Cauchy problem that is settled by the nonlinear viscous Burgers equation. The viscous Burgers equation is a partial differential equation that is encountered in fluid dynamics studies, particularly in the domain of upward flow. The simplified model of the viscous Burgers equation explains the behavior of incompressible viscous fluid. The inverse Burgers problem belongs to a class of problems called ill-posed problems, which implies that there may be multiple sets of initial and/or boundary conditions that result in the same solution of the Burgers equation. To obtain robust and reliable solutions, it is essential to use regularization and cross-validation methods. However, it is often difficult to solve analytically, so numerical approaches are developed to overcome this difficulty. Domain decomposition (DDM) was used with alternative iterative methods. We performed a numerical reconstruction of the velocity and normal stress tensor that were vanished on an inaccessible part of the boundary using the over-prescribed noisy data obtained on the other accessible part of the boundary.

Neutrosophic set is a modern branch as a generalization of fuzzy concept.  Zadeh in 1965 presented fuzzy concept and later he introduced more applications in more subjects of mathematics.  On of the type branch of mathematics is fuzzy algebra. In this work, we present and clarify several results of several modules, which has zero-kernel, and zero homomorphism in neutrosophic theory. The aim modules are mnonoform and small monoform modules.  Several concepts have been studied in this paper like Quasi-dedekind and uniform modules.  We proved that if ( ( )) is a module over neutrosophic ring ( ). If ) is a directed sum of simple submodules an  is monoform, then ) is monoform module.  Also, if  𝒯) is a semi simple ring and  𝒯) is a  𝒯)-module, so  𝒯) is small and satisfies all conditions of monoform with Q-dedekind property. On the other hand, let be an R-module. is a neutrosophic modules and generated by  and . So, is a weak neutrosophic. Finally, we presented more results, examples and properties about the topic with new results in neutrosophic algebra.