Communications in Mathematics and Applications

Rough \(\Delta^m\)-Statistical Convergence of order \(\alpha\) of Generalized Difference Sequences in Intuitionistic Fuzzy Normed Spaces

Gursimran Kaur — 2025-08-20

The prime direction of this research article is to explicate the perception of rough \(\Delta^m\)-statistical convergence of order \(\alpha\) of generalized difference sequences in intuitionistic fuzzy normed spaces. We showed certain rough convergence features, which give some new functional tools in the face of uncertainty, such as intuitionistic fuzzy normed spaces. We demonstrated some basic properties and examples which generates the results that this perception is more generic. Further, we added the set of \(\Delta^m\)-statistical limit points and set of \(\Delta^m\)-statistical cluster points and their relationship of rough \(\Delta^m\)-statistically convergence of generalized difference sequences in these spaces.

A New Robust Application for Singularly Perturbed Volterra-Integro Differential Equations

Derya Arslan — 2025-08-20

In this study, we aimed to approximately solve singularly perturbed Volterra-integro differential equation with the Adomian decomposition method. The solution procedure is easy and fast. Firstly, the equation is written in operator form. Then the integral operator is applied to all sides of the equation. The series solution is obtained by applying some operations to the given equation and then converting it into a recurrence relation. Error values show that the solution results obtained for the two applied examples are very close to each other. The proposed method gives successful results with 21 and 23 iterations.

Philos-Type Criteria for Testing the Oscillatory Performance of Solutions to Differential Equations With a Natural Argument

Ahmed E. Amer — 2025-08-20

The oscillatory performance of nonlinear delay differential equation solutions \((b \psi (u) [w']^r) '+q u^\beta (\varrho) =0\) is examined in this work. The canonical case is considered, and Philos-type criteria are established to test the oscillation of all solutions. The existence of \(\phi\) increases the difficulty in obtaining the asymptotic and monotonic properties of the solutions and also increases the possibility of applying the results to a broader range of special cases. The results obtained in this study represent an extension and generalization of earlier findings in the literature.

Generating Functions of a New Class of Semi-Orthogonal Polynomials \(X_n (x ; a,\alpha)\) Using Lie Group Theory

R. R. Jagtap — 2025-08-20

In this paper, by applying the group theoretic method introduced by Weisner, we determined new generating relations of a new class of semi-orthogonal polynomials \(X_{n} (x;a,\alpha)\). By giving proper analytical reasoning to the index \(m\) of the semi-orthogonal polynomial, we derived three linear partial differential operators with the help of the ascending and descending differential recurrence relation of the polynomial. These linear partial differential operators generate a Lie group.

Lie Symmetry Analysis, Exact Traveling Wave Solutions by \(\left(\frac{G'}{G}\right)\)-Expansion Method and Qualitative Analysis of Hirota-Schrödinger Equation

Arshdeep Kaur — 2025-08-20

This manuscript is based on the Hirota's equation with Kerr law nonlinearity, specifically contemplated to be a kind of nonlinear Schrödinger equation. A systematic investigation of Lie symmetry method is pertained to derive the symmetry reduction of the given equation. By utilizing these symmetry reductions, the nonlinear partial differential equation is altered into the ordinary differential equations. By utilised the \(\big(\frac{G'}{G}\big)\)-expansion technique to gain exact solutions of the Hirota-Schrödinger equation. Novel solitary wave solutions were successfully extracted, characterized by hyperbolic, rational, and trigonometric function forms. Furthermore, a qualitative analysis of the reduced system is performed by converting it into an autonomous system, allowing the investigation of the stability and behavior of critical points. Several phase portraits are presented for various parameter values to illustrate the system's dynamics.

A Note on Multiplicative Fuzzy on BP-Algebras

V. Abisha — 2025-08-20

Multiplicative fuzzy sets are defined by combining the membership values of the elements in a fuzzy set. This can be considered a generalization of fuzzy sets. Multiplicative fuzzy sets are useful in areas like quantum mechanics. In this paper, we define multiplicative fuzzy BP-algebras using the multiplication operation on membership functions and investigate some of their properties. Multiplicative fuzzy topological BP-algebras are also discussed.

Performance Assessment of Production Inventory System With Catastrophes Including Negative Customers and Machine Breakdowns

A. Abi Shunmuga Kanni — 2025-08-20

This study looks at a production inventory system that experiences breakdowns in machines, negative customers and catastrophes. If a customer arrives and raises their level in the waiting hall with a probability of \(r\), they are considered ordinary; if they drop their level without inventory with a probability of \(1-r=\bar{r}\), they are known as negative customers. Upon completion of service, a customer exits the system, causing the inventory level to decrease by one. Catastrophic events force the inventory level to drop to zero. The production policy is \((s, S)\), where \(S\) is the fixed maximum inventory level. A machine could break down during production, in which case it will be fixed at random. The steady-state joint probability distribution of the inventory level, the number of customers in orbit, and the machine status are derived using the matrix-geometric method. Several performance measures are calculated, and the results are used to develop a cost function. Finally, numerical results are presented to demonstrate the system's behavior.

Arithmetic Subderivatives Relative to Subsets of Primes

Champak Talukdar — 2025-08-20

The arithmetic derivative is a number-theoretic function that behaves analogously to differentiation defined on integers. In this paper, we extend the concept to generalized arithmetic subderivatives with respect to a chosen set of primes. Inspired by the work of P. Haukkanen (Generalized arithmetic subderivative, Notes on Number Theory and Discrete Mathematics 25(2) (2019), 1 – 7), we introduce a family of arithmetic functions that generalize the prime-power exponents in the classical definition. We establish necessary and sufficient conditions under which these generalized subderivatives satisfy analogs of linearity, the Leibniz rule (product rule), and multiplicativity. Several illustrative examples are worked out to demonstrate the computations and properties of these subderivatives.

Dynamic Queueing Model for Smart Manufacturing: A Priority-Based Performance Study

Balveer Saini — 2025-08-20

In this paper, we present a Dynamic Priority Queueing Model (DPQM), which effectively solves the problems of traditional queueing models in complex priority scheduling situations in manufacturing systems. The DPQ paradigm uses priority functions, time-based queueing, and advanced scheduling algorithms to schedule tasks elegantly. The priority function swiftly prioritizes tasks based on urgency, relevance, and resource demands, adapting to changing circumstances. The~suggested \(M(t)/G(t)/c\) queueing model extends the \(M/G/c\) model for real-world applications with time-dependent task arrivals and service activities. The model validation and implementation process enable efficient calculations of priority values, lead time, tardiness, usage, and efficiency. The average lead time is 179 minutes, tardiness is 106 minutes, and resource utilization is 100%. The scheduling efficiency improves by 17.6% by effectively sequencing activities to match system priorities. The validation shows that the model prioritizes work and properly maps changing parameters compared to traditional queueing systems. The results indicate that improving adaptive scheduling, real-time feedback systems, and using multiple servers can maximize resource utilization to generate high throughput and eliminate work delays. This approach serves as a robust and adaptable strategy for dynamic scheduling, thoughtfully considering priorities within complex manufacturing environments.

Integral Transforms of Pragathi-Satyanarayana’s \(I\)-function

B. Satyanarayana — 2025-08-20

Many of the transformations like Euler, Hankel, Sumudu and \(K\)-transforms play a vital role in the field of engineering mathematics and have many applications. This paper refers to the study of Pragathi-Satyanarayana \(I\)-function of one variable. As a part of this study, we obtain different integral transforms of Pragathi-Satyanarayana \(I\)-function of one variable. Also, some of the~generalized transforms have been obtained as special cases. The integral transformations developed here are useful in real-world applications of mathematical science.

A Examining Fuzzy Partial Metric Space and Associated Outcomes

Renu P. Pathak — 2025-08-20

Using the concept of a PM space with fuzzy, it gives idea of a FPMS in this paper. A point’s self-distance in partial metric space does not always equal to zero. Ordinary metric is a subset of partial metric. Additionally, also define continuous t-norms. Partial fuzzy contraction mapping is defined here. It also demonstrates that, in certain circumstances, the complete partial metric space has a common fixed point through use of contraction mapping. Relevant examples are used as provide results.

Intuitionistic Fuzzy Sets and its Application in Carrier Determination by the Fusion of Score Function and Normalized Hamming Distance Method

Ruchi Trivedi — 2025-08-20

Intuitionistic fuzzy sets are commonly used to solve decision making problems. In this paper, a new score and accuracy function of intuitionistic fuzzy sets have been proposed, and used to solve the carrier determination problems. The fusion of score function and normalized hamming distance method of intuitionistic fuzzy sets have been used to determine the distance between each students and each carrier. The results of this approach were then analyzed to determine the most suitable career paths for each student based on their individual characteristics and preferences.

An Enhanced Intrusion Detection Classification Approach for Securing IoT Networks

Fayez Alharbi — 2025-08-20

The research investigates different classification methods that IDS developers use for developing intrusion detection systems. Recent rapid growth of internet of things (IoT) devices created a massive surge in available data requiring highly effective methods for preventing malicious activities. The research attempts to boost IDS effectiveness through ML algorithm implementation to obtain precise intrusion classification and identification. The research group obtained assessment data through three datasets which included IoT-Modbus and IoT-Fridge and IoT-Weather to measure classification frameworks’ abilities when detecting different threats affecting IoT systems. For the IoTFridge dataset, the one-vs-one (OvO) classification reached 100% accuracy; for the IoT-Weather and IoT-Modbus, the accuracy was 99.7% and 77.62%, respectively. The one-vs-rest (OvR) classification method yielded accuracies of 100% for IoT-Fridge data, 98.02% for IoT-Weather, and 77.62% for IoT-Modbus. The performance results on IoT-Modbus and IoT-Fridge datasets were comparable between OvO and OvR methods while OvO produced slightly superior results on the IoT-Weather dataset. The research demonstrates that multi-class classification techniques demonstrate outstanding performance for IDS systems which can boost IoT application cybersecurity capabilities. The major objective of this research is to introduce a new IDS system with enhanced potential of detecting threats in IoT environments, while handling specific IoT protection obstacles.

Closeness Centrality Weight of Graphs Under Some Graph Operations

Veena Mathad — 2025-08-20

Many complex systems exhibit a natural hierarchy in which elements can be ordered according to a notion of influence with closeness centrality being one of the three well-known centrality measures used in social network analysis, determining the importance of vertices in a network, a core task in each network application. It describes the relative importance of a single vertex within a network or graph by finding the average proximity of that vertex to all others in that graph. In this paper, we derive formulae for the closeness centrality weight of the graph resulting from the operations between some graph families namely, join graph, Cartesian product of graph, shadow graph, corona graph, lexicographic product, disjunction graph and total graph.

Combinatorial Properties of the Difference Set With Respect to CPHMs of Row Sum 0 and 2

Pankaj Kumar Manjhi — 2025-08-20

This article investigates the combinatorial properties of difference sets within the cyclic group \(\mathbb{Z}_n\), specifically in the context of Circulant Partial Hadamard Matrices (CPHMs). We examine the structural characteristics and establish relationships between difference sets associated with \(2\text{-}H(m \times n)\) and \(0\text{-}H(m \times n)\) matrices. Our results provide insights into the interplay between these matrix classes and their corresponding difference sets, contributing to the broader understanding of their applications in combinatorial design theory.

A New Modified Integral Transform

H. L. Tidke — 2025-08-20

We introduce a new modified integral transform – a comprehensive extension encompassing the classical Laplace transform and its variants developed in recent decades. We establish its fundamental properties, including existence, linearity, scaling, shifting (both first and second), differentiation, integration, periodicity, and convolution. As a unifying framework, simplifies and generalizes various known integral transforms. We demonstrate its effectiveness through solutions to ordinary and partial differential equations, Volterra integral equations, partial integro-differential equations, and systems of ODEs, supported by illustrative examples.

Redundancy Optimization for a System Comprising Two Operative Unit and \(N\) Cold Standby Units with Activation Time

Parveen Kumar — 2025-08-20

A well-known idea in the field of reliability engineering is the use of standby redundancy to raise a system’s reliability and maximize profitability, ensuring the sustainability of economies and industries. To accomplish this, a reliability model is developed that incorporates a finite number \((N)\) of cold standby units, in addition to two operational units, taking into account the activation time required to transition a standby unit to an operational state. Upon failure of either operational unit, a cold standby unit is activated to assume its responsibilities, functioning with equivalent effectiveness. The system operates with two working units at a time and if in any state there is only one operative unit available, then the system works at reduced capacity. The determination of the required number of standby units involves establishing cut-off points based on factors such as revenue, failure rates, installation costs, activation rates, etc. Computational analyses have been conducted to facilitate this process, incorporating Markov processes and various performability measures. The regeneration point technique is employed to optimize the number of standby units.

An Analytical Approach for a Deterministic Epidemiological Model – Monkeypox Clinical Disease

J. Sujatha — 2025-08-20

In this study, we investigate a non-linear differential equation modeling the transmission dynamics of monkeypox. We begin with a thorough stability analysis to assess the equilibrium points of the model, providing insights into the conditions under which the disease may persist or diminish within a population. Following this, we employ the q-Homotopy Analysis Transform Method (q-HATM) to derive analytical solutions, showing its effectiveness in handling the complexities inherent in non-linear systems. Our findings reveal that while both methods yields valuable insights into the behavior of the monkeypox transmission model, q-HATM offers greater flexibility in terms of initial conditions and non-linearity. This work contributes to the understanding of monkeypox for future research in disease modeling using advanced mathematical techniques.

Some Properties of Pythagorean Fuzzy Normed Ideals

Manish Kumar Gunjan — 2025-08-20

Pythagorean fuzzy sets are an advanced extension of fuzzy sets, building upon the framework of intuitionistic fuzzy sets and offering a more comprehensive solution to the limitations inherent in intuitionistic fuzzy theory. This study introduces the concept of Pythagorean Fuzzy Normed Ideals (PFNIs). It explores the intrinsic product between two PFNIs, presenting key results related to this operation. Additionally, the study introduces the concept of characteristic functions in the context of PFNIs and discusses several significant properties of these functions. Furthermore, important findings concerning the epimorphism of Pythagorean fuzzy normed ideals are also presented.

\(H\)-\(E\)-Super Magic Graceful Labelings of Graphs

Duraisamy Kumar — 2025-08-20

This article examines H-E-Super Magic Graceful Labelings (H-E-SMGL) of graphs. These labelings provide a systematic way to analyze how graphs can be decomposed into subgraphs with specific properties, particularly in the context of H-coverings. We investigate several families of graphs, including fans, books, and grids admits H-E-SMGL.

Fermatean Picture Fuzzy Continuity in Fermatean Picture Fuzzy Topological Spaces

V. Chitra — 2025-08-20

The purpose of this paper is to define a new Picture fuzzy continuous mapping in Fermatean picture fuzzy topological spaces and investigate its fundamental properties. In addition, we explore a key topological concept FPF-\(\beta\) connectedness within the framework of Fermatean picture fuzzy topology.

Intuitionistic Fuzzy Binary Soft Topological Spaces

Vyshakha Elluru — 2025-08-20

In this article, intuitionistic fuzzy binary soft topological space over two initial universal sets and a parameter set is introduced. Further, intuitionistic fuzzy binary soft neighborhood, intuitionistic fuzzy binary soft interior, intuitionistic fuzzy binary soft closure in an intuitionistic fuzzy binary soft topological space is defined, and their properties are discussed.

An Investigation of the Bifurcation of Traveling Wave Solutions in Time-Fractional Nonlinear Differential Equations of the Symmetric Case

Mustafa T. Yaseen — 2025-08-20

This study considers examining and bifurcation of traveling wave solutions in time-fractional nonlinear differential equations of the symmetric case. We blend Li and He’s derivative of fractional order techniques with Lyapunov-Schmidt reduction in our approach. To simplify the analysis, the initial fractional equation that is differential is transformed into a partial differential equation through the utilization of the fractional complex transform. This conversion results in a condensed equation, presented as a pair of nonlinear algebraic equations, tackling the core issue. Furthermore, our investigation involves examining linear approximation solutions for a nonlinear fractional equation (NFE) that is differential.

Higher-Order Numerical Techniques for Solving the Nonlinear Fisher Equation are Based on the Runge-Kutta Method

Richa Kumari — 2025-08-20

This paper presents higher-order numerical methods for solving nonlinear Fisher equations. These types of equations arise in various fields of sciences and engineering, the main application of this equation has been found in the biomedical sciences. The solution of this equation helps to determine the size of the brain tumor. In this paper explores the utilization of advanced numerical techniques, such as the method of lines and higher-order strong stability preserving schemes of order four and stage seven, to approximate solutions to the Fisher equation with higher-order accuracy. These schemes are explicitly designed and easy to implement, especially for addressing nonlinear problems. Their stability-preserving nature ensures only mild restrictions on time steps. This scheme is then tested on two examples and the results show that it is more efficient methods and requires less computing time. Various test problems are examined to verify the scheme’s performance, including a comparison of l2 and l∞ errors with the exact solution, leading to high accuracy.