https://mcs.qut.ac.ir/ Mathematics and Computational Sciences en daily 1 Fri, 06 Feb 2026 00:00:00 +0330 Fri, 06 Feb 2026 00:00:00 +0330 https://mcs.qut.ac.ir/article_734002.html This study presents a fractional-order malaria transmission model based on a ten-compartment structure that incorporates Caputo derivatives to capture memory effects in disease dynamics. The model distinguishes non-immune and semi-immune human populations alongside mosquito compartments. We establish mathematical properties including existence, uniqueness, positivity, and boundedness of solutions within a biologically feasible region. An explicit expression for the basic reproduction number R0 is derived using the next-generation matrix approach, and stability conditions for disease-free and endemic equilibria are analyzed via the Matignon criterion. Numerical simulations under realistic parameter settings demonstrate that decreasing the fractional order α delays epidemic peaks, reduces infection intensity, and prolongs disease persistence, highlighting the significant influence of memory effects on malaria dynamics. These results confirm that fractional-order models provide a more accurate representation of transmission patterns compared to classical integer-order frameworks. https://mcs.qut.ac.ir/article_734003.html This study presents a numerical method based on Radial Basis Functions (RBFs) for solving a class of fractional optimal control problems. First, the necessary optimality conditions are derived in the form of a system of two fractional differential equations. Then, by solving an associated system of algebraic equations, an approximate solution to the problem is obtained. The fractional derivative considered in this study is the Caputo fractional derivative. Several examples are provided to demonstrate the effectiveness of the proposed method and to compare the accuracy of the resulting numerical solutions. https://mcs.qut.ac.ir/article_735178.html Difference equations are discrete analogy of the differential equations. These equations appearin mathematical modeling of physics and engineering problems, economic and population subjects thatdeal with discrete data and variables.In this article, we consider and solve these types of equations that are non-homogeneous and non-linear.The solving method is performed using by multiplicative discrete and continuous differential equations.The importance of this method is that by using the concept of discrete derivative, the analytical methodand analytical solutions are given to linear and non -linear non-Homogeneous difference and differentialequations. https://mcs.qut.ac.ir/article_734009.html This study introduces a 24-note numerical framework and computational method to explore connections among music, mathematics, the theory of four temperaments, and zodiac constellation. While earlier research has acknowledged these links, it lacked formal mathematical structures and systematic validation. The 24-note system is significant in two respects. First, it validates the existing 17-note system. Second, it establishes a crucial theoretical foundation for microtones. By providing this solid groundwork, it challenges the conventional Western musical framework, which is confined to tones and semitones, and paves the way for the practical application of microtones in fields such as music therapy, where their potential has remained largely untapped. Despite differences in numbers, results show complete agreement between the 24-note and 17-note systems in analyzing scales within Iran’s seven main musical modes (Dastgāh). The study reveals that structural symmetry can identify symmetrical scales, but only when the sum of the "Valued Numbers" (Manzeli) within one tetrachord equals the sum within the other tetrachord. It also introduces an entirely novel and invaluable relational model that connects musical notes to the four classical elements and planets. Research demonstrates that note the "LA'' functions as the foundational reference, with the position of all other notes calibrated relative to it. Finally, it presents the Cyclic Boundary Theorem (CBT), a novel mathematical concept that offers two complementary computational approaches for the systematic numerical evaluation of partitioned cyclic systems. https://mcs.qut.ac.ir/article_735179.html ‎This study investigates the existence of solutions for certain systems of integral equations in multi-component models with asymmetric and ‎heterogeneous dynamics‎, ‎using fixed point theory‎. ‎Classical metric frameworks are not sufficiently flexible to adequately capture these systems‎, ‎highlighting the need for more flexible‎‏ ‎approaches‎. ‎To address these challenges‎, ‎a Perov-type vector-valued metric space endowed with a triangle inequality controlled by two matrices is introduced‎, ‎which extends classical metric‎ ‎frameworks by incorporating two independent control matrices‎. ‎This double-controlled structure significantly enlarges the admissible class of mappings and allows component-wise control adapted to heterogeneous dynamics. Within this setting, the concept of $\mathbb{M}_\alpha$-admissible pairs of selfmaps is defined, and new common fixed point theorems under generalized matrix-type contraction conditions are established, extending several existing results in the literature. ‎The proposed methodology is applied to a two-dimensional integral equation system‎, ‎and a numerical example is presented to validate the theoretical results‎.‎‎ https://mcs.qut.ac.ir/article_735243.html This article investigates the time-space fractional advection-dispersion equation $(TSFADE)$. In this work, an efficient and precise numerical method (Novel Bernoulli Operational Matrix technique) is applied for solving a category of these equations, converting the original problem into a set of algebraic equations that can be solved using numerical methods. The key benefit of this scheme is its ability to transform linear and nonlinear $(PDEs)$ into a set of algebraic equations concerning the expansion coefficients of the solution. The suggested scheme is effectively utilized for the mentioned problem. Sufficient and thorough numerical evaluations are provided to illustrate the precision, applicability, effectiveness, and adaptability of the introduced scheme. To showcase the efficacy and accuracy of this technique, the numerical results from the examples are expressed in a table format to enable comparison with results from other established methods as well as with the precise solutions. It should be noted that the implementation of the current method is regarded as quite simple. https://mcs.qut.ac.ir/article_733004.html This study examines an economic model and explores the Hopf bifurcation by individually varying the indebtedness factor and the output-capital ratio parameter. Both analytical and numerical methods are used to determine the conditions and coefficients for the normal form of the Hopf bifurcation. The critical coefficient for this bifurcation is identified using the central manifold theory. Additionally, the phase portrait of the model near the critical values of the indebtedness factor and the output-capital ratio parameter is illustrated using the Matcont software package. https://mcs.qut.ac.ir/article_735244.html This study aims to investigate a fractional-order mathematical model that describes smoking behavior, formulated using the Caputo fractional (CF) derivative. which effectively captures long-term memory effects the population is divided into five compartments: potential smokers, current smokers, occasional smokers, permanent quitters, and temporary quitters. The model incorporates several parameters characterizing transition rates between these compartments, allowing for a realistic simulation of smoking dynamics. To obtain efficient approximate solutions, we present a new hybrid approach, both analytical and numerical, which combines the specific general integral transform with the homotopy perturbation method (HPM). Numerical simulations performed in MATLAB for different fractional orders reveal the high precision and numerical performance of the proposed technique. Graphical analyses further highlight the method’s effectiveness in capturing the temporal evolution of the model, confirming the reliability of the hybrid approach in representing such complex dynamical systems. https://mcs.qut.ac.ir/article_735306.html Quantum graphs provide a rigorous framework for modelling quantum dynamics on network-like structures, where edges represent one-dimensional wires and vertices encode interaction conditions. Since their introduction as models for wave propagation and molecular systems, quantum graphs have grown to become an essential tool in mathematical physics, providing information on spectral, transport, and scattering phenomena. The mathematical foundations of quantum graphs are reviewed in this review, covering self-adjoint operators, metric graph formalisms, and vertex conditions that control the behaviour of wave functions. Next, we discuss important developments in spectrum theory that make quantum graphs strong models for quantum chaos and universal spectral statistics, including resonance features, eigenfunction statistics, and spectral gap optimisation. Stability analyses and inverse spectrum problems broaden the theoretical scope of the framework, while extensions to leaky, transparent, and random quantum graphs show how versatile it is. The survey emphasises the function of quantum graphs as a link between discrete and continuous models by combining these viewpoints. We conclude by describing open difficulties in the areas of spectral invariants and random graph models. https://mcs.qut.ac.ir/article_735567.html Fermatean Quadripartitioned Neutrosophic fuzzy graphs (FQNFG) is the integrating form of Fermatean and Quadripartitioned Neutrosophic fuzzy graphs. Graph energy is recognized as a crucial concept in fuzzy graph theory for its ability to handle random events, thus capturing the attention of numerous researchers. Moreover, the study of graph energy has been a notable rise in recent years. Energy of Graphs have significant applications in various domains, including network analysis, decision making, Image processing, modelling uncertainty etc. This paper introduces energy and Laplacian energy for FQNFG. Adjacency matrix, eigen values, energy and Laplacian energy of FQNFG are defined with suitable illustrations. Furthermore, we obtain lower and upper bounds of energy and Laplacian energy for FQNFG. Additionally, this study presents a decision-making method that uses a scoring approach to assess and compare Laptops based on critical attributes such as processing power, memory & storage, Battery life and Display quality. https://mcs.qut.ac.ir/article_733024.html Two-person games have been extensively studied in classical game theory, but uncertainty and imprecision in real-world scenarios necessitate more advanced mathematical frameworks. Pentapartitioned Neutrosophic sets, provide a powerful tool for handling contradiction, ignorance, unknown, and inconsistent information. This paper explores two-person games in a Pentapartitioned Neutrosophic environment, where players’ strategies, payoffs, and outcomes are expressed using Pentapartitioned Neutrosophic numbers. We present fundamental definitions, solution concepts, and equilibrium conditions tailored for such games. The findings demonstrate that Pentapartitioned Neutrosophic game theory provides a more flexible and realistic approach to strategic interactions involving indeterminacy. https://mcs.qut.ac.ir/article_735566.html Integral transform methods are effective techniques for addressing a range of dynamic equations characterized by initial or boundary value conditions, frequently expressed in the form of integral equations. This article presents the ET on an arbitrary timescale $\mathbb{T}$ as a new integral transform for addressing specific problems. The ET on timescales appears absent from the existing literature. This new approach primarily unifies discrete and continuous analysis, allowing for the treatment of differential, difference, and $q$-difference equations within a singular framework. This study's results pertain to ordinary differential equations for $\mathbb{T} = \mathbb{R}$, difference equations for $\mathbb{T} = \mathbb{N}_0$, and $q$-difference equations for $\mathbb{T} = q^{\mathbb{N}_0}$, where $q^{\mathbb{N}_0} = \{q^t | t \in \mathbb{N}_0 ~\text{for}~ q >1\} $ which hold significant relevance in quantum theory. The proposed transform can be applied to various nonstandard timescales, including $\mathbb{T} = h\mathbb{N}_0$, $\mathbb{T} = \mathbb{N}^{2}_{0}$, and $\mathbb{T} = \mathbb{T}_n$, which represent the space of harmonic numbers. Numerous examples and applications illustrate the efficacy of the ET on timescales in addressing dynamic equations. https://mcs.qut.ac.ir/article_735569.html This paper presents a computational framework for estimating stride rate in football using advanced computer vision and deep learning techniques, integrating modules for player detection, tracking, team identification, pitch mapping, and performance analysis. Convolutional Neural Networks (CNNs) are used for spatial feature extraction, while YOLOv8 enables accurate player detection, and a Kalman filter supports robust multi-object tracking by modeling player motion as continuous trajectories in two-dimensional Euclidean space. Player kinematics are derived by computing velocity as the time derivative of position and total distance as the cumulative displacement between frames. The system incorporates AlphaPose for anatomical keypoint detection, allowing precise motion capture, and models periodic movement using sinusoidal functions to estimate stride frequency. To enhance accuracy, the Savitzky–Golay filter is applied for trajectory smoothing. Experimental evaluation on broadcast football footage demonstrates strong performance, achieving 93.1% consistency in stride rate estimation, a 90.3% success rate, and an error margin below 2%. Additionally, the integration of digital twinning technology enables real-time visualization of player movements, supporting applications in performance optimization, fatigue monitoring, and injury prevention, thereby advancing automated sports analytics through data-driven decision-making. https://mcs.qut.ac.ir/article_735575.html This study develops an economic order quantity model that accounts for advance payment schemes, deterioration, and preservation technology in an intuitionistic fuzzy environment to capture real-world inventory uncertainty. The proposed model further integrates demand, which depends on the selling price, advertising frequency, and stock levels, along with time-varying holding costs, allowance for partial backorders, and the impact of inflation. First, the crisp model is formulated, and then the triangular intuitionistic fuzzy number is applied to this model. Defuzzification of the fuzzy model is performed using two distinct approaches: the signed distance method and the graded mean integration representation method. A solution procedure is developed to determine optimal solutions, and an algorithm is created by combining the results of all models derived from the analytical study. The numerical example is illustrated for both the crisp and fuzzy models, and 2D and 3D graphs are plotted using MATLAB (R2025a).A sensitivity analysis examines how changes in inventory parameters affect the optimal solution, offering managers valuable insights for decision-making under uncertainty. https://mcs.qut.ac.ir/article_735274.html This article presents and investigates the novel model of a balanced Fermatean Quadripartitioned Neutrosophic Fuzzy Graphs, based on density functions. We examine the intrinsic properties of these graphs, focusing on the necessary conditions for Fermatean Quadripartitioned Neutrosophic Fuzzy Graphs (FQNFG) to achieve balance, particularly under self-complementary, complete, and strong graph characteristics. Additionally, we analyze the properties of FQNFG complements, providing insights into their structural relationships and transformations. Finally, we apply this theoretical foundation to model student performance, addressing uncertainties and complexities in educational data. Leveraging balanced FQNFGs provides clearer and fairer insights into student performance, enabling targeted interventions and supporting more effective with equitable educational practices. https://mcs.qut.ac.ir/article_735275.html In this work, we show that the fixed points of β − ψ weakgeneralized ciric-type rational contraction mappings for a pair of metricsprovided by a dIGraph are identical. We provided examples and machinelearning applications to back up our conclusions https://mcs.qut.ac.ir/article_733601.html In this paper, we study the mean ergodic theorems and the weighted ones on locally compact hypergroups. Among other obtained results, for the class of all commutative hypergroups $\mathcal{H}$ with a Plancherel measure $\widetilde{\omega}$ that ${\rm supp}(\widetilde{\omega})=\widehat{\mathcal{H}}$, we prove that if $\left(k_{j}\right)_{j \in \mathbb{N}}$ is a subsequence of $\mathbb{N}$, $f\in L^2(\mathcal{H})$, and $\mu$ is a power bounded measure on $\mathcal{H}$ such that the sequence$$\left(\frac{1}{m} \sum_{n=1}^{m}\underbrace{\mu\ast\ldots\ast\mu}_{k_{n}-\text{times}}\ast f\right)_{m\in\mathbb{N}}$$weakly converges in $L^2(\mathcal{H})$, then the numerical sequence $\left(\frac{1}{m} \sum_{n=1}^{m} \alpha^{k_n}\right)_{m\in\mathbb{N}}$ is convergent too for all $\alpha\in \mathbb{C}$ with $\tilde{\omega}\left(\{\xi\in\widehat{\mathcal{H}}:\hat{\mu}(\xi)=\alpha\}\right)>0$. https://mcs.qut.ac.ir/article_733603.html First and foremost, securing the electoral process is fundamental to public trust in democratic governance. Traditional voting systems, from paper ballots to electronic machines, have long survived despite vulnerabilities to tampering, limited auditability, and an absence of strong end-to-end verifiability. To address these, this paper proposes the Secure and Transparent Blockchain Voting Algorithm (STBVA), a blockchain-based voting system powered by Proof of Authority (PoA) consensus, elliptic curve cryptography (ECC), and homomorphic encryption. Accordingly, PoA can support deterministic fast block production with low computational overhead, which makes it suitable for regulated election environments. In particular, ECC offers efficient authentication for users, while Paillier homomorphic encryption keeps votes private during tallying processes without revealing individual ballots. The proposed system is implemented and evaluated on a permissioned blockchain network consisting of seven validators and 20 full nodes, accommodating up to 500,000 simulated voters. Experimental results show that confirmation latency is 1.2 s at median, the sustained throughput is 1200 tps, and the accuracy of end-to-end vote recording is 99.8\%. Thereafter, a formal attacker model, security claims, and proof sketches corroborate the resilience against forgery, double voting, and ledger manipulations. The results underpin that STBVA is able to achieve scalable, privacy-preserving, and tamper-resistant election infrastructure to cater for national-level online voting. https://mcs.qut.ac.ir/article_733604.html This paper introduces neutrosophic nano β-continuous functions and explores their fundamental properties in neutrosophic nano topological spaces. The study establishes their role in extending continuity concepts for handling uncertainty and indeterminacy. https://mcs.qut.ac.ir/article_733606.html The main purpose of this paper is to present a novel concept of separation axioms in neutrosophic topological spaces by means of neutrosophic N_tr Λ_P-open sets. The concepts of neutrosophic N_tr Λ_P-T_i spaces(i=0,1,2) are introduced and their properties are studied.  https://mcs.qut.ac.ir/article_733627.html This work introduces a novel set, the Intuitionistic Complex Fuzzy Set (ICFS), that expands traditional intuitionistic fuzzy sets into a complex-valued domain and captures interacting attributes more effectively in the decision support framework based on ICFS. A new aggregation operator called the Intuitionistic Complex Fuzzy Einstein Correlated Geometric (ICFECG) operator and a new score and accuracy function for the ICFS are proposed and to ensure theoretical robustness, rigorous proofs are provided for multiple theorems associated with the newly developed ICFECG operator, the score and the accuracy functions. This operator effectively combines expert opinions while preserving both the amplitude and phase components of complex uncertainty, thereby ensuring that the aggregated information accurately reflects the full structure of the intuitionistic complex fuzzy evaluations. To improve efficiency in solving MAGDM problems, a data mining–based dimensionality reduction strategy that helps identify and remove redundant or weakly influential attributes is introduced. Artificial Neural Network (ANN) techniques are also incorporated to enhance the learning ability and optimization of the decision-support process. A new defuzzification function is proposed to integrate all the ICFS components, yielding a crisp value for enhancing the data mining and ANN computations. The final hybrid model combines ICFS theory, the ICFECG operator, data mining, and ANN optimization which effectively handles high-dimensional, correlated, and uncertain information arising in the decision making environment. A numerical case study shows that our methodology reduces the computational load, removes insignificant alternatives, and significantly improves decision accuracy, stability, and reliability. https://mcs.qut.ac.ir/article_733634.html This paper addresses Multi-Criteria Group Decision Making (MCGDM), also known as Multiple Attribute Group Decision Making (MAGDM), under the framework of intuitionistic fuzzy sets. To solve fuzzy linear algebraic equations, linear space techniques involving real eigenvalues are employed. These solutions are then used to determine decision-maker weights in MAGDM problems. During the weight determination process, multiple criteria are explicitly incorporated, and several results obtained through the proposed methods are normalized. Additionally, decision-maker weights for attributes, along with corresponding decision-making approaches, are introduced. Furthermore, Artificial Neural Network (ANN) techniques are applied to enhance the determination of decision-maker weights. The feasibility and effectiveness of the proposed approach are demonstrated through numerical examples. The convergence curve shows stable error reduction without underfitting or overfitting, validating the robustness of the proposed ANN framework for reliable application in intuitionistic fuzzy set–based MAGDM. https://mcs.qut.ac.ir/article_733708.html The utilization of the Indian rail system has grown at a very high rate and there is one of the largest train track networks in the world in the country. Despite the creation of various sophisticated means of transport, congestion, inefficiency and bad connectivity remain factors to contend with. To overcome these challenges, the metro rail has beendiscovered to be the most possible urban mass transit system and can be easily modeled using graph theory with vertices represented by stations and edges by tracks. In this paper, we begin by examining traditional metrics like connectivity, complexity, diameter,average distance between the terminals and potential expansion of the network in the hopeof quantifying passenger convenience and efficiency. We also advance the research withnew concepts: vertex and edge domination are used to compute the minimum criticalstation for effective surveillance, vertex and edge connectivity to quantify survivability against failure and labeling or coloring techniques for use with scheduling, traffic control and resource allocation. This joint approach results in both classical and new findings for more resilient metro network planning and construction. https://mcs.qut.ac.ir/article_733774.html This paper introduces a novel operational matrix approach for addressing a class of fractional-order optimal control problems, where the derivative is taken in the regularized Prabhakar sense. The method employs Bernoulli polynomials and utilizes their operational matrix of regularized Prabhakar derivative and inherent properties to convert the original problem into a finite-dimensional optimization problem. Using the Lagrange multiplier approach, the required optimality conditions are derived, yielding an algebraic system from the original problem. Solving this system yields an approximate fractional optimal solution. The practicality and efficiency of the proposed approach are confirmed via a series of numerical examples. https://mcs.qut.ac.ir/article_733783.html This paper investigates the concept of locally harmonious coloring in the context of high-dimensional interconnection net works, specifically the hypercube Qn, its structural variants such as the folded hypercube FQn, the augmented cube AQn, and the crossed cube CQn. We aim to determine χlh(Qn), χlh(FQn), χlh(AQn), and χlh(CQn), and to analyze how dimensional variations and structural augmentations influence their locally harmonious colorability. Furthermore, we establish relationshipsbetween χlh and other graph invariants such as degree, diameter, and automorphism group symmetry. The study provides new insights into the combinatorial structure of hypercube-based networks and their applications in parallel architectures, fault tolerant communication, and distributed computation. https://mcs.qut.ac.ir/article_733842.html Benzenoid systems are formed by collections of congruent hexagons arranged in the plane such that any two hexagons are either disjoint or share a common edge. These structures are naturally studied through graph-theoretic packing parameters. For a fixed graph H, an H-packing of a graph G is a family of vertex-disjoint subgraphs of G, each is isomorphic to H. In this work, we determine the P3- packing number and an induced P3-packing k-partition number for three standard benzenoid families: the triangular benzenoid system, the rhombic benzenoid system, and the zigzag benzenoid system. For each class, algorithmsare provided for computing these parameters, together with justification of their correctness. The results yield exact values for the corresponding packing and partition numbers in these benzenoid structures. https://mcs.qut.ac.ir/article_733856.html The thermal diffusion coefficient in radioactive materials is not a constant value, and this makes the heat transfer problem different in such materials and materials that are not homogeneous and have been destroyed or are disintegrating in some way. In the problem under discussion, the heat diffusion coefficient is time-dependent and satisfies a nonlinear integral equation. The existence and uniqueness of the solution to the integral equation in question are discussed in detail in Chapter 13 of the Book "Encyclopedia of the One-Dimensional Heat Equation" by Cannon, J. R. The integral equation in question is not a standard Volterra integral equation and therefore has not been studied much from a numerical perspective. For example, if we apply the fixed point method, which is a powerful tool in the analysis of existence and uniqueness, discussed in Chapter 13 of the aforementioned Book, to a numerical solution, we cannot go even one step forward with this method. Since the unknown function is located at the kernel of a nested integral, applying canonical methods becomes difficult. Therefore, in this paper, we have discussed a hybrid method of numerical integration and iterative methods that solves the problem with sufficient accuracy. In Section 5, we have extracted several sample problems using the properties of the heat equation in the case where the thermal diffusivity is Time-dependent. The numerical solution of these sample problems in the Section 6 demonstrates the efficiency and accuracy of the proposed method. https://mcs.qut.ac.ir/article_733857.html The Birkhoff polytope graph can be considered as the Cayley graph of the symmetric group $S_n$ with respect to $\mathcal{C}_n$, the set of cycles in $S_n$. Since the degree of every Cayley graph is a natural bound on several parameters of the graph, in this note by presenting a formula for $|\mathcal{C}_n|$, the degree of the Birkhoff polytope graph, we prove that it is bounded from above by$\lfloor e\big{(}(n-1)! +(n-2)!+(n-3)! +\cdots 1 \big{)}\rfloor$, where $e$ is the Neper number. https://mcs.qut.ac.ir/article_733944.html This paper investigates boundary value problems for the fractional Pauli operator on a finite square domain, addressing a significant gap in the literature where such problems have not been previously studied. The fractional Pauli operator generalizes the standard Pauli operator by replacing the classical Laplacian with the fractional Laplacian (−∆)α=2, introducing non-local quantum effects. We employthe spectral definition of the fractional Laplacian on bounded domains, expanding the solution as a double trigonometric series that automatically satisfies Dirichlet boundary conditions. The problem is reduced to solving a linear algebraic system for the series coefficients, for which we prove existence and uniqueness in appropriate fractional Sobolev spaces. Numerical experiments for various fractional ordersα demonstrate significant deviations from the classical case (α = 2), with solutions exhibiting enhanced amplitudes and diffusive characteristics as α decreases. Rigorous convergence analysis establishes the continuous transition to the classical Pauli operator as α ! 2−. https://mcs.qut.ac.ir/article_735725.html The quantification of similarity between fuzzy objects is central to decision-making and clustering under uncertainty. While numerous measures have been developed within Intuitionistic, Pythagorean, and Fermatean fuzzy frameworks, these approaches cannot be directly applied to Complex Fermatean Fuzzy Sets (CFFSs) because CFFSs represent membership and nonmembership degrees through complex amplitudes and phases. This study proposes novel similarity measures specifically designed for CFFSs, establishes their fundamental mathematical properties, and demonstrates their performance through applications in decision-making and clustering. The results confirm that the proposed measures effectively capture complex-valued uncertainty and provide a reliable foundation for practical fuzzy analysis.