Damghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904Convergence Quantum Analysis of Positive Solution for Caputo-Hadamard Fractional $q$-Differential Equations204219211910.22128/ansne.2026.3296.1210ENMohammad Esmael SameiDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran0000-0002-5450-3127Somayeh NazariDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranJournal Article20260413In this research we obtain new results of approximate solution for nonlinear singular $p$-Laplacian Caputo-Hadamard fractional $\mathtt{q}$-differential equation under infinite-point boundary conditions. The existence of unique iterative positive, error estimation, and convergence rate of approximate solution are obtained based on the description of Green function with special properties and employing appropriate substitution and appropriate cone. A few applications are demonstrated the validity of our achievements.https://ansne.du.ac.ir/article_2119_b0c81babd3acde4395ac30eaf59f7655.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904Artificial Neural Network and Physics-Informed Neural Network Assisted Analytical Solutions for Nonlinear Fractional Biological Models Using Local Fractional Operators220237212010.22128/ansne.2026.3304.1212ENN. RamyaDepartment of Mathematics, Kongu Engineering College, Erode, India0009-0005-1665-1996Maryam AkhoundiClinical Research Development Unit of Rouhani Hospital,
Babol University of Medical Sciences, Babol, Iran0000-0002-2419-1732Mostafa NouriJouybariPayame Noor University (PNU), Tehran, IranFarshid MofidnakhaeiDepartment of Physics, Sari Branch, Islamic Azad University, Sari, Iran0000-0002-2903-0428Journal Article20260421This study presents a hybrid computational framework integrating analytical methods, artificial neural networks (ANN), and physics-informed neural networks (PINNs) for solving nonlinear fractional biological models governed by local fractional operators. In contrast to conventional approaches, the proposed framework incorporates local fractional calculus to effectively represent fractal and heterogeneous biological structures. An analytical solution is first derived using the Natural transform in conjunction with the Adomian decomposition method, yielding closed-form expressions in terms of Mittag--Leffler functions. This analytical formulation is subsequently utilized as a knowledge-driven prior to train an ANN-based surrogate model, thereby improving convergence efficiency and reducing computational complexity. Furthermore, a physics-informed neural network is constructed by embedding the governing fractional differential equation into the loss function via a Gr"unwald--Letnikov approximation, enabling accurate learning of long-memory effects without requiring explicit analytical solutions. Comparative analysis with classical numerical solutions obtained using the \texttt{bvp4c} solver demonstrates that the ANN surrogate achieves high-accuracy predictions with error magnitudes below $\mathcal{O}(10^{-4})$ while reducing computational cost by approximately 45\%. The PINN framework further exhibits strong capability in capturing intrinsic fractional dynamics under limited data conditions. Overall, the proposed ADM--ANN--PINN hybrid architecture provides a robust, efficient, and physically consistent framework for modeling complex nonlinear fractional biological systems, thereby advancing the state-of-the-art in fractional computational intelligence.https://ansne.du.ac.ir/article_2120_2b1c9ab4c6d0bbfca261411e6c7b484e.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904Development and Analysis of Optimized Numerical Scheme for Three-Dimensional Linear Time-Fractional Diffusion Equations238247212110.22128/ansne.2026.3291.1208ENMahdi EmamjomehBasic Science Group, Golpayegan College of Engineering, Isfahan University of Technology, Golpayegan, 87717-67498, Iran.0000-0002-5557-463XJournal Article20260314In this paper, an optimized numerical method for solving time-fractional diffusion equations in three-dimensional space is proposed. Fractional-order differential equations can model complex physical processes with memory effects more accurately than differential equations with integer order derivatives. On the other hand, numerical solutions of this type of problem are usually challenging due to the existence of a singularity near the initial time. In the proposed method, in order to overcome this issue, the $L1$ formula has been used on a graded mesh to maintain the accuracy of calculations near the initial time. Also, a fourth-order compact operator has been used to discretize the Laplace operator in three-dimensional space. Stability and convergence analyses show that this method has a convergence order proportional to the grading parameter in time and a fourth-order convergence order in space. The obtained results from numerical simulations confirm the high accuracy of the proposed method and the efficiency of the optimal selection of the scaling parameter in achieving the suitable convergence order, even in the presence of initial singularities.https://ansne.du.ac.ir/article_2121_9f2d1ac9be5de9daa5f70db95a8b5ca0.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904A Multi-Layer Graph-Theoretic Model for Detecting Anomalous Communication Patterns in IoT Networks248272212310.22128/ansne.2026.3266.1199ENAliakbar Tajari SiahmarzkoohDepartment of Computer Sciences, Golestan University, Gorgan, IranJournal Article20260216The rapid proliferation of Internet of Things (IoT) devices has created complex network environments increasingly vulnerable to sophisticated cyber attacks. Detecting anomalous communication patterns in such heterogeneous networks requires mathematical models capable of capturing the multi-faceted nature of IoT traffic. This paper develops a multi-layer graph-theoretic framework for detecting anomalous communication patterns in IoT networks. The proposed model represents network traffic as a multi-layer graph where each layer corresponds to a different communication modality including TCP, UDP, ICMP, HTTP, and MQTT. Unlike prior works that assume stationary Poisson processes, we propose a dynamic negative binomial model with an overdispersion parameter to capture burstiness and a time-varying function to model diurnal patterns. The framework integrates three complementary mathematical approaches: spectral analysis using random matrix theory for global structural anomalies, local neighborhood analysis using graph signal processing for node-level behavioral deviations, and inter-layer correlation analysis using tensor decomposition for coordinated multi-vector attacks. To ensure practical robustness under non-stationary conditions, we introduce permutation-based threshold calibration that controls false positive rates even when theoretical assumptions are violated. Comprehensive sensitivity analysis is provided for all hyperparameters including integration weights, time window length, and tensor rank. Fair comparative evaluation is conducted against six state-of-the-art graph-based methods including Graph Convolutional Networks (GCN), Dynamic Graph Neural Networks (DyGNN), Multi-layer Graph Convolutional Networks (M-GCN), GraphSAGE, Graph Attention Networks (GAT), and Ensemble Graph Convolutional Networks (E-GCN). Numerical experiments on real IoT traffic datasets from CICIDS2017 and Bot-IoT demonstrate that the proposed framework achieves a detection rate of 89.2\% with a false positive rate of 3.8\%, outperforming the leading baseline M-GCN by 1.7\% in detection rate. The computational complexity scales linearly with network size, enabling near real-time deployment in large-scale IoT environments.https://ansne.du.ac.ir/article_2123_7bfdee19939ae5083c01bfb174cceabf.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904An Efficient LASSO Estimation for Time‑Dependent Cox Models via Adaptive Active‑Set Coordinate Descent273288212610.22128/ansne.2026.3301.1211ENRohollah RamezaniDepartment of Statistics, Faculty of Mathematical Sciences,
Shahrood University of Technology, Shahrood, Iran0000-0002-9158-9708Mohammad RezaRabieiDepartment of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran0000-0003-4647-8002Mohammad ArashiDepartment of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran.0000-0002-5881-9241Journal Article20260417The penalized Cox proportional hazard model is a popular analytical approach for survival data with a large set of covariates. Such problems are especially challenging when covariates vary over follow-up time (i.e., the covariates are time-dependent), leading to increased computational complexity and difficulties in efficient variable selection. In this paper, we propose an Adaptive Active-Set Coordinate Descent (AACD) algorithm for LASSO-penalized time-dependent Cox models. The proposed method combines coordinate descent with an adaptive active-set strategy and warm starts along the regularization path, allowing the algorithm to focus computation on relevant variables and better exploit sparsity. Simulation studies demonstrate that AACD consistently outperforms \texttt{glmnet}, achieving uniformly lower mean squared errors with relative efficiency greater than one across all settings, and reducing estimation error by up to 37\% in small samples. The method remains robust as dimensionality increases, improves variable selection by reducing false negatives, and produces more parsimonious models with comparable predictive performance while reducing runtime by approximately 36\% in real data analysis.https://ansne.du.ac.ir/article_2126_4913bc1120573bdc831089efb0a02f42.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904Fuzzy Regression-Based Statistical Modelling of Cardiovascular Risk Factors Using Indian Healthcare Data289303212510.22128/ansne.2026.3328.1218ENMaheswari DDepartment of Mathematics, Sri Krishna Arts and Science College, Coimbatore, Tamil Nadu, India0009-0007-1079-080XGopinath MDepartment of Mathematics, Sri Krishna Arts and Science College, Coimbatore, Tamil Nadu, India0009-0005-8665-7701Alimohammad Fallah AndevariDepartment of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, IranMostafa NouriJouybariPayame Noor University (PNU), Tehran, Iran0000-0003-2295-1504Farshid MofidnakhaeiDepartment of Physics, Sar.C., Islamic Azad University, Sari, Iran0000-0002-2903-0428Journal Article20260522Cardiac disease is a major public health concern in India, and accurate statistical techniques are required for early risk assessment. Traditional regression analysis generally depends on fixed clinical thresholds; however, cardiovascular risk factors such as blood pressure, cholesterol, diabetes, obesity, tobacco use, and physical activity involve uncertainty because they gradually move from the absence of risk to the presence of risk. This study applies fuzzy regression to develop a statistical modelling framework for analysing cardiovascular disease risk factors using the Heart Attack Risk and Prediction dataset from Kaggle. The proposed modelling process includes data preprocessing, descriptive analysis, fuzzy membership construction, fuzzy regression modelling, and comparison with conventional regression models. The selected clinical and lifestyle variables are transformed into linguistic risk levels such as low, moderate, and high risk, thereby allowing the uncertainty associated with individual risk profiles to be represented more meaningfully. The performance of the models is evaluated using statistical measures such as mean absolute error, root mean square error, accuracy, sensitivity, specificity, and receiver operating characteristic area under the curve. The fuzzy statistical modelling approach improves interpretability and provides a flexible risk assessment structure compared with conventional modelling methods. Overall, this study presents a fuzzy regression-based statistical framework to support data-driven cardiovascular risk assessment in the Indian healthcare context.https://ansne.du.ac.ir/article_2125_4399b42131606c6171446a63ac8ec928.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904A Comparative Study of Regular Expression Tools for Developers: Usability, Practical Efficiency, and a Nonlinear Equation Case Study304310212710.22128/ansne.2026.3287.1207ENSeyed Hashem TabasiSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran0000-0002-0110-2856Saba GhorbaniDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranAtiyeh Mohammadi MotlaghDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranSetareh Hashempour MohammadabadDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranZahra Rezaei BoroonDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20260306Regular expressions (regex) play a fundamental role in modern software development, enabling efficient data validation, text processing, and pattern matching across a wide range of applications. Despite their versatility, the intricate syntax and abstract structure of regex patterns often create significant challenges for developers, particularly in terms of construction, debugging, comprehension, and maintenance. To address these issues, specialized regex development and debugging tools have been introduced to improve usability and reduce development effort. This study presents a qualitative comparative analysis of widely used regex tools, including Regex101, RegExr, Debuggex, and RegexBuddy, together with an assessment of regex support provided by modern integrated development environments (IDEs). The evaluation is conducted with respect to key usability criteria, including learnability, ease of use, debugging support, visualization capabilities, and workflow integration. In addition, a practical case study is presented in which regex-based techniques are employed to parse and extract structural components of nonlinear mathematical equations. The case study demonstrates the effectiveness of these tools in facilitating complex pattern recognition, improving program comprehension, and supporting software analysis tasks. The results indicate that the choice of an appropriate regex tool can significantly enhance developer productivity, reduce debugging effort, and improve the overall understanding of complex regular-expression patterns. These findings provide useful guidance for both practitioners and researchers seeking effective tool support for regex-intensive software development activities.https://ansne.du.ac.ir/article_2127_a1391fe0473994a4f9512a03e8f19311.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260901A Hybrid Numerical Scheme for the Time-Fractional Telegraph Equation311323212810.22128/ansne.2026.3271.1201ENSeyyedeh Mitra DabiriDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, IranJavad DamirchiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran0000-0002-4878-1921Journal Article20260218This study introduces a hybrid approach based on a finite difference scheme and radial basis functions (RBF) for solving the Caputo time-fractional telegraph equation numerically. To handle the temporal fractional derivatives, a finite difference formulation of the L1/L2 type is adopted, while the spatial derivatives are approximated using an RBF collocation technique. This combination results in a discretized system characterized by a sparse matrix structure. Through the application of energy methods, the stability and convergence assessment of the temporal discretization is conducted, yielding a theoretical error estimate of $\mathcal{O}(\delta_t^{3-\alpha})$ in the time direction. The reliability and effectiveness of the proposed numerical scheme are verified through a representative test problem, confirming the capability of the proposed method to achieve high accuracy.https://ansne.du.ac.ir/article_2128_1cbc3e4f1dd2e3b2347a517cf5c9c26e.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260901Bootstrap Highest Density Confidence Interval by Comparing Two Climatological Regions324332213210.22128/ansne.2026.3310.1214ENAli ShadrokhDepartment of Statistics, Payame Noor University, P.O.Box 19395-4697, Tehran, Iran0000-0003-0069-8165Mehdi PejmanDepartment of Statistics, Payame Noor University, P.O.Box 19395-4697, Tehran, IranJournal Article20260506Bootstrap is a resampling method based on high calculations, which can help us a lot for statistical inference in cases where the amount of data that we have is limited. For example, in the design of hydraulic structures such as bridges or dams, etc. there is a need to estimate hydrological events such as, floods or precipitations by statistical inference of quantiles of a probability distribution. In this paper, we aim to estimate precipitation quantiles. For calculating this estimation, the confidence interval for quantiles has been introduced with percentile bootstrap, accelerated bias-corrected bootstrap, t-bootstrap methods; that in this article, we want to compare these methods with the confidence interval made by the highest density method based on bootstrap data and we obtain the average length of the confidence intervals as a criterion to evaluate the methods. To calculate the average length of confidence intervals using different methods, first, the best distribution among commonly used distributions is fitted to the original data, and its parameters are estimated using the maximum likelihood method, and quantiles are obtained from it. Then, we continue until the coverage probability of the real quantile reaches the nominal confidence level of 95$\%$ by repeating the simulated bootstrap samples. The results of the performed simulation show that the bootstrap highest density method has the smallest average length of confidence intervals among all methods. The data used in the article are 24-hour annual maximum precipitation records in five meteorological stations in Mexico, which are compared with the data of five stations in Gilan province of Iran.https://ansne.du.ac.ir/article_2132_81dc48da06120a6111f5afe7cde2fdb7.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904A Hybrid Method Based on Rational Legendre Physics Informed Neural Networks and Cuckoo Optimization Algorithm for Solving Nonlinear Inverse Partial Differential Equations333351213910.22128/ansne.2026.3307.1213ENFarhad FahimiSchool of Mathematics and Computer Science, Damghan University, Damghan, IranReza PourgholiSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran0000-0003-4111-5130Abdolali BasiriSchool of Mathematics and Computer Science, Damghan University, Damghan, IranJournal Article20260429We develop an improved physics-informed neural network (PINN) framework for solving nonlinear inverse partial differential equations. Two separate network architectures are explored: one utilizing Legendre polynomials as activation functions and another employing rational Legendre polynomials. In the latter case, there is a crucial hyperparameter, $L$, that significantly impacts both performance and efficiency. To optimize this parameter, we employ the cuckoo optimization algorithm (COA), which fine-tunes $L$ based on the problem's characteristics. The proposed methods are tested on two benchmark problems, the Fisher equation and the Burgers--Fisher equation. The results highlight the effectiveness of both approaches, demonstrating superior accuracy in reconstructing unknown boundary conditions. All experiments were conducted in a Jupyter Notebook environment using PyTorch, confirming the potential of tailored activation functions and optimization techniques in physics-informed deep learning.https://ansne.du.ac.ir/article_2139_4e39992c98f2436f7ce0ff0abdca8ab2.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904Simultaneous Profit Optimization and Market Price Agreement in Networks of LTI Duopoly Systems352362214110.22128/ansne.2026.3344.1221ENMehrasa AyatollahiDepartment of Mathematics, Payame Noor University, Tehran, Iran0000-0003-0542-7137Journal Article20260601This paper studies networks of dynamic duopoly systems with the objectives of maximization of firms' discounted profits and of convergence of market prices in all markets. We model each duopoly as a dynamical process of price adjustment, driven by production decisions of firms. The profit maximization problem is reformulated as a quadratic optimal control problem by representing the dynamics of the duopoly in a linear time-invariant (LTI) state-space form. In order to impose the price convergence between the markets, a consensus term is added to the cost function. We use the Hamilton--Jacobi--Bellman (HJB) approach to derive a control law that encourages profit maximization and market price convergence over a finite time horizon. The proposed framework reformulates the dynamic duopoly problem in networked markets within an optimal control framework, allowing simultaneous profit optimization and market price coordination.https://ansne.du.ac.ir/article_2141_1c1a9ca486183d2e93d538ee2cc3eff2.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X11220260904A Globally Convergent Fixed Point Framework for Linear and Nonlinear Mechanical Vibration Systems363374215410.22128/ansne.2026.3360.1225ENParvin TorabiDepartment of Mathematics,
Faculty of Basic Sciences,
Jundi-Shapur University of Technology,
Dezful, IranJournal Article20260616A rigorous fixed-point framework is developed for linear and nonlinear second-order mechanical vibration systems governed by ordinary differential equations with damping, stiffness, external forcing, and nonlinear restoring forces. The governing equation is reformulated as a Volterra operator equation in an appropriate Banach space, yielding a convenient integral formulation for constructing a Picard fixed-point iteration. Global existence, uniqueness, and convergence are established under suitable contraction conditions, with explicit bounds on the contraction constant and the corresponding geometric convergence rate of the iterative sequence. Energy-based stability estimates are derived for both forced and unforced systems, providing bounds on the mechanical energy and clarifying the dissipative behavior of the underlying dynamics. A discrete quadrature-based implementation of the Volterra formulation is developed and analyzed in terms of convergence order and stability properties under appropriate conditions. Numerical experiments for representative linear and nonlinear vibration problems are presented to validate the theoretical findings and to demonstrate the accuracy, convergence, and effectiveness of the proposed fixed-point approach.https://ansne.du.ac.ir/article_2154_073e705585a2ce688642a1dbcfdd8492.pdf