University of GuilanJournal of Mathematical Modeling2345-394X14320260801Modelling size dependent bending behavior of cracked magneto electro piezoelectric nanobeam under hygro-thermal loads803820940310.22124/jmm.2026.31394.2819ENSelvapandiMuthulakshmiResearch scholar, Karunya UniversityRajendreanSelvamaniDepartment of mathematics ,Karunya university, Coimbatore ,IndiaFarzadEbrahimiMechanical Engineering department, Faculty of engineering, Imam Khomeini International
University, Qazvin, IranJournal Article20250813This study is focused on the bending response of electro-magneto-elastic nanobeams exposed to hygro-thermal environments while resting on a Winkler–Pasternak elastic foundation, utilizing non local elasticity theory. The governing equations are formulated within the framework of parabolic third order shear deformation beam theory and derived using Hamilton’s principle. An open crack is modeled as a rotational spring to represent its local flexibility, and its influence is integrated into the analytical solution. A comprehensive parametric study examines how the nonlocal parameter, crack severity and position, aspect ratio, hygro-thermal and magneto-electro-mechanical loadings, influence the deflectionn characteristics of nanobeams. The findings reveal that cracks, boundary conditions, nonlocal effects, and beam geometry significantly influence the dimensionless deflection behavior of nanoscale structures.https://jmm.guilan.ac.ir/article_9403_969b668663f30d561d96a45367c7ff06.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Fractional-order modeling and numerical simulation of diphtheria transmission in Rohingya refugee settlements using the fractional Adams-Bashforth-Moulton method821844940410.22124/jmm.2026.31992.2892ENMd NurulRaihenDepartment of Mathematics and Statistics, University of Toledo, OH, USAMd AbdulKadirDepartment of Mathematics, University of Houston, TX, USAVinodhChellamuthuDepartment of Mathematics, Utah Tech University, UT, USAMansoorAlsulamiFaculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaJournal Article20251018Fractional order derivatives have become increasingly significant in mathematical modeling of infectious disease dynamics due to their ability to capture memory and hereditary properties of biological processes. In this study, we adopt and analyze a fractional order Susceptible-Latent-Infectious-Recovered (SLIR) model to investigate the spread of diphtheria among the Rohingya refugee population in Bangladesh. The model incorporates the Caputo definition of the fractional derivative and is solved numerically using the Fractional Adams-Bashforth-Moulton method (FABMM). Model parameters, including disease transmission and recovery rates, are estimated using available epidemiological data. The impact of varying the fractional order and other key parameters on the progression and control of the outbreak is explored through comprehensive numerical simulations. Graphical representations of daily and cumulative case trajectories for different fractional orders are presented, highlighting the effectiveness of fractional modeling in forecasting and controlling outbreaks. The results suggest that fractional order models provide more flexible and realistic predictions compared to classical integer-order approaches. These findings can aid the Bangladeshi government and humanitarian organizations in developing effective disaster response and public health strategies for preventing and managing diphtheria outbreaks.https://jmm.guilan.ac.ir/article_9404_53c05978bc1dfddce88eb10fac88a8d5.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Optimal location of healthcare and treatment centers with complex structures based on performance845859940510.22124/jmm.2026.31510.2834ENAzamAzodiFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.JafarFathaliFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.MojtabaGhiyasiFaculty of Industrial Engineering and Management Science, Shahrood University of TechnologyTahereSayyarFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.Journal Article20250826Optimal use of existing facilities and resources to improve the efficiency of healthcare and treatment centers, achieving social welfare, and responding to the needs of customers, is an important issue. Paying more attention to healthcare and treatment centers, allocating sufficient resources, and using them correctly will improve the health of the workforce and increase production and productivity in society. One of the important mechanisms for evaluating the performance and efficiency of healthcare and treatment centers is the use of data envelopment analysis. In this article, we propose a new mechanism for the proper distribution of facilities and healthcare and treatment centers in cities to reduce costs and also maximize the efficiency of healthcare and treatment centers with the aim of better quality of services. This is done by integrating the problem of -median location and network data envelopment analysis. Proposed methods are applied for performance measurement, location-allocation, and distribution of 11 healthcare and treatment centers in Shahrood. The primary results show potential of cost reduction that could be done when allocating clients, considering the performance of healthcare and treatment centers. Another important finding is to have centralized healthcare and treatment centers rather than diffused center to reach the optimal condition which is a vital information for health care policy makers.https://jmm.guilan.ac.ir/article_9405_ef9c1962249bf1180aaa1b177937d05f.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801On mathematical modeling and stability analysis of chickenpox models in the presence of weakened-immune individuals in a population861890940710.22124/jmm.2026.31347.2812ENCharles IwebukeNkekiDepartment of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Edo State, NigeriaImuwahen AnthoniaMbarieInstitute of Child Health, College of Medical Sciences, University of Benin, Benin City, Edo State, NigeriaJournal Article20250807The varicella-zoster virus (VZV) also known as chickenpox is one of the most contagious diseases. Individuals who have never had VZV, have never been vaccinated, or have a compromised immune (which is refers to as immunocompromised) systems, stand the highest risk of VZV infection. This paper considers susceptible-exposed-infectious-weaken immune-recovered-vaccinated (SEIWRV) epidemic model for chickenpox infectious disease, in the presence of treatment. The basic reproduction number, denoted by ${\cal R}_o$ for the model is obtained, and found to be re-enforce by two classes of individuals: -spread from the first-time infected and unvaccinated individuals, and spread by the weaken-immune individuals. This basic reproduction number depends on incidence rate from the susceptible and weaken-immune individuals as well as treatment rate. It is shown in this paper that the model exhibits two equilibria, which include, the disease-free and the endemic equilibriums. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on number of infectious, ${\cal R}_o$ and the treatment rate. The global endemic equilibrium is established using geometric approach, which is applied to a five-dimensional system of differential equations. We found that chickenpox will remain endemic as long as weaken-immune individuals remain in the population. Numerical simulations are also presented to illustrate our main results. It is found that it is possible to eradicate chickenpox from the population, only if the medical practitioners and researchers understand the role of weaken-immune individuals in the spread of chickenpox.https://jmm.guilan.ac.ir/article_9407_81deb2727379fa04e0f4893c892e0aaa.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801A stable and convergent fully discrete scheme for solving two-dimensional distributed-order fractional cable models891907942110.22124/jmm.2026.32479.2945ENHamidRezaeiDepartment of Mathematics, College of Sciences, Yasouj University, Yasouj-, 75914-74831, IranMeysamAsadipourDepartment of Mathematics, College of Sciences, Yasouj University, Yasouj-75914-74831, IranMohammad HosseinDerakhshanDepartment of Mathematics, College of Sciences, Yasouj University, Yasouj-75914-74831, IranJournal Article20251208This paper investigates a novel distributed-order time-fractional cable equation involving both Caputo and Riemann–<br />Liouville fractional derivatives, which models complex diffusion and memory effects in various physical and biological systems. The proposed model incorporates a distributed-order fractional Laplacian term, a memory integral, and a nonlinear source, capturing multiscale temporal dynamics and nonlocal behavior. A robust numerical scheme is developed by applying a fractional Adams–Bashforth–Moulton predictor-corrector method for time discretization, while central difference approximations are used for the spatial Laplacian. This results in a fully discrete scheme that effectively combines the advantages of convolution quadrature with classical finite difference methods. A detailed convergence and stability analysis of the numerical method is presented using an energy-based approach and a discrete fractional Gronwall inequality. The method is proven to be unconditionally stable and achieves optimal convergence<br />rates in both time and space. Numerical simulations confirm the theoretical predictions and demonstrate the accuracy<br />and efficiency of the scheme in capturing the underlying fractional dynamics. The proposed framework offers a powerful<br />and flexible tool for the numerical simulation of fractional-order systems with distributed memory, and can be extended<br />to a wide range of multi-term and distributed-order fractional partial differential equations.https://jmm.guilan.ac.ir/article_9421_1b45020e2f34cc4e3e7e8e1335df757d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Implementation of a meshless method for optimal control of elliptic variational inequality909922942610.22124/jmm.2026.31996.2891ENMahmoodKhaksar-e OshaghDepartment of mathematics education, Farhangian University, Tehran UniversityJournal Article20251016In this paper, a mesh-free method is presented for the numerical solution of an optimal control problem constrained by an elliptic variational inequality. The proposed method is indirect and based on the element-free Galerkin method to solve the considered nonlinear optimal control problem. First, the optimality conditions of the problem are derived via the Lagrangian technique. The obtained conditions are mixed complementarity conditions which can be solved by specific efficient algorithms. Here, the moving least squares approximation is utilized within the element-free Galerkin approach to numerically solve the obtained optimality conditions. The proposed method is mesh-free and can be used with irregular meshes and even in irregular domains. Finally, The convergence of the proposed method is numerically investigated and results confirm high-order accuracy.https://jmm.guilan.ac.ir/article_9426_f2a61aaa49b68fc736320d00edb30132.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801A mathematical study on reaction-diffusion model in biomedicine923940942910.22124/jmm.2026.32423.2938ENVembuAnanthaswamyThe Madura College (Autonomous -Affiliated to Madurai Kamaraj University, Madurai )JeyakumarAnantha JothiResearch Scholar, Research Centre and PG Department of Mathematics, The Madura College (Autonomous)
Madurai, Tamil Nadu, IndiaMoorthiSubhaDepartment of Mathematics
Fatima College (Autonomous)
Madurai, Tamil Nadu, IndiaJournal Article20251219The present investigation examines the Michaelis-Menten kinetics response diffusion problem in a planar, spherical framework by employing mathematical model. The substrate concentration is found to have straightforward outcomes with the Michaelis constant, modified Sherwood number, and Thiele modulus. Here, the analytical approximation for the non-dimensional substrate concentration and unitless effectiveness factor are determined via the new approximate<br />analytical methodology for steady-state (Ananthaswamy-Sivasankari method ASM) and Homotopy with Laplace transform method for non-steady state. Additionally, juxtaposition between the analytical approximation and numerical simulation is provided. There is a good correlation between the numerical results and the approximate analytical result.https://jmm.guilan.ac.ir/article_9429_26d7d68dad2ec6caa1c3eaabd8d01b2c.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801An improved nonlinear conjugate gradient method and its application to satellite image restoration941951945210.22124/jmm.2026.30611.2744ENAtefeBayDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranZohrehAkbariDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandran, Babolsar, IranJournal Article20250510In this paper, an improved nonlinear conjugate gradient method is proposed for solving unconstrained optimization problems. Due to the high computational cost of Newton-type methods, conjugate gradient methods have emerged as efficient alternatives for large-scale problems. However, their performance heavily depends on the choice of search directions and algorithmic parameters. In the proposed method, a novel parameter and a modified search direction are introduced to ensure sufficient descent at each iteration. Global convergence of the method is established under standard assumptions. Numerical experiments on satellite image restoration demonstrate the superiority of the proposed method over the Polak–Ribiere–Polyak method in terms of noise reduction and image quality enhancement.https://jmm.guilan.ac.ir/article_9452_6f9144f776637490ba9d046afc0c7b22.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801HyEMST: A novel hybrid ellipsoidal framework for robust clustering via maximum spanning trees953983945410.22124/jmm.2026.32457.2943ENHosseinEyvaziDepartment of Computer Science, Tarbiat Modares University, Tehran, IranSeyed MohammadBadzohrehDepartment of Computer Science, Tarbiat Modares University, Tehran, Iran0009-0009-4488-581XAmir MohammadKharaziDepartment of Computer Science, Tarbiat Modares University, Tehran, IranJournal Article20251204Clustering arbitrary-shaped clusters with heterogeneous densities presents a fundamental challenge in unsupervised learning. Traditional approaches emphasize either geometric distance or local density estimation, yet rarely reconcile both perspectives systematically. This paper introduces HyEMST (Hybrid Ellipsoidal Maximum Spanning Tree), a principled framework that unifies distance and density information through an explicit trade-off parameter λ ∈ [0,1]. The proposed methodology comprises five phases: (1) strategic geometric decomposition via K-Means over-segmentation; (2) robust volumetric density estimation using adaptive ridge-regularized covariance; (3) hybrid kernel construction integrating distance and density affinities; (4) topological structure discovery via maximum spanning tree; and (5) adaptive density-aware cluster merging. Theoretically, we establish that regularized covariance-based density estimation preserves density ranking with > 90% accuracy, ensuring reliable merging even for ill-conditioned micro-clusters. Computationally, the approach achieves O(N d2 ) overall complexity. Empirically, HyEMST attains perfect or near-perfect clustering on synthetic benchmarks and demonstrates superior performance compared to representative baselines on real-world datasets. Ablation studies validate the necessity of hybrid integration and confirm the efficacy of each algorithmic component.https://jmm.guilan.ac.ir/article_9454_7ae292cc67050b50fc70fc1bc1b47f59.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Convergence and stability analysis of fractional integral residual minimization method for fractional differential equations and system of fractional differential equations9851004947710.22124/jmm.2026.31926.2881ENSyed BahurudeenRiyasdeenDepartment of Mathematics, Khadir Mohideen College, Adirampattinam, Tamil Nadu, IndiaAyyaduraiTamilselvanDepartment of Mathematics, Bharathidasan University, Tiruchirapalli, Tamil Nadu, IndiaSekarElangoDepartment of Mathematics, Amrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, IndiaJournal Article20251009In this article, we propose a Fractional Integral Residual Minimization Method (FIRMM) to solve Fractional Differential Equations (FDEs) with the Caputo derivative. We provide a detailed and rigorous study of convergence analysis and stability analysis of FIRMM under suitable assumptions. Also, we extend the method FIRMM to solve a class of system of Caputo FDEs with a detailed and rigorous study on convergence analysis and stability analysis under suitable assumptions. The efficacy of our proposed method is established through numerical experiments. The advantages and limitations of FIRMM are analyzed.https://jmm.guilan.ac.ir/article_9477_3804129becb5c8093e1dfda06f452fe8.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Variance minimization in resource leveling for self-financing project portfolios: a convex MIQCP approach10051025949710.22124/jmm.2026.31598.2845ENSeyed MahdiMirkhorsandi LangaroudiDepartment of Civil Engineering, Ne.C., Islamic Azad University, Neyshabur, Iran.HosseinKhosraviDepartment of Civil Engineering, Hakim Sabzevari University, Sabzevar, IranAlirezaDavoodiDepartment of Mathematics, Ne.C., Islamic Azad University, Neyshabur, IranSeyed MojtabaMovahedifarDepartment of Civil Engineering, Ne.C., Islamic Azad University, Neyshabur, IranJournal Article20250904This study addresses the critical trade-off between financial returns and operational stability in capital-intensive project portfolios. We propose a novel convex Mixed-Integer Quadratically Constrained Programming (MIQCP) framework that unifies Net Present Value (NPV) maximization, strict self-financing, and direct resource variance minimization. Unlike existing non-convex or heuristic models, our approach endogenizes flexible phasing strategies and introduces a dual-buffer mechanism to protect both liquidity and resource capacity. By exploiting the positive semi-definite properties of the quadratic constraints, we ensure global optimality for portfolios with 50+ activities. Computational results reveal a significant ”constrainedness” effect, where tighter financial and precedence constraints accelerate convergence by pruning the search tree. Findings demonstrate that a negligible NPV sacrifice (< 2%) yields disproportionate gains in resource stability (> 8%), providing a high-fidelity decision-support tool for managing internal capital markets under high volatility.https://jmm.guilan.ac.ir/article_9497_05f1d25348b3811bab743c8c7705c80d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801A bi-level optimization model for an ambulance routing problem for green, red, and black patients in a post-disaster stage10271051949810.22124/jmm.2026.32560.2959ENRahelehKhanduziDepartment of Mathematics and Statistics, Faculty of Basic Science and Engineering, Gonbad Kavous University, Gonbad Kavous city, golestan province, iranJournal Article20251216In post-disaster environments, effective allocation and routing of ambulances is crucial to minimize casualties and improve overall emergency response efficiency. This paper develops a novel bi-level programming model to address the ambulance routing problem with triage-based patient categorization, including green, red, and black patients. The upper level focuses on strategic decisions regarding ambulance allocation and dispatching, while the lower level models operational routing decisions performed by responders. The proposed approach integrates triage priorities, limited resources, and road network disruptions, yielding a realistic framework for decision support. A hybrid solution methodology based on Genetic algorithm, tabu search, and teaching learning based optimization is presented. Experimental results on test instances from existing literature demonstrate the model's capability to balance response time efficiency and prioritization of critical patients.https://jmm.guilan.ac.ir/article_9498_cd8a97be997cfd12e273a12836a9aa40.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Determination of control parameter in an inverse time fractional diffusion equation using a linearized fourth-order finite difference scheme10531069954310.22124/jmm.2026.32796.2986ENAkbarMohebbiDepartment of Applied Mathematics, Faculty of Mathematical Science, University of Kashan, Kashan, IranBehnamSalehiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer, Semnan University, Semnan, IranJournal Article20260113The problem of finding the space- or time-dependent control parameter in partial differential equations has increasingly appeared in physical phenomena, for example, in the study of control theory, heat conduction process, and chemical diffusion. This study aims to construct an efficient numerical method to determine a time-dependent source term in a time fractional diffusion equation subject to over-specification at a point in the spatial domain. We use a second order scheme to discretize the equation in the time direction, then we replace the space derivative with a fourth-order compact finite difference approximation. We will construct a linearized difference scheme and prove the solvability, and unconditional stability of the proposed method. Due to the usually ill-posed nature of inverse problems, we examine the stability of the method with respect to perturbations of the data. We show that the proposed method achieves stable and accurate numerical approximations without using any regularization techniques. Numerical experiments show satisfactory results for problems with smooth, non-smooth, and discontinuous initial conditions.https://jmm.guilan.ac.ir/article_9543_800b76e4142fd15876e9467c6323087d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801An investigation on transmission and control of fractional-order hepatitis B model10711091954410.22124/jmm.2026.31885.2878ENDeepak-Department of Mathematics, Vivekananda Global University JaipurLokesh KumarYadavDepartment of Mathematics, Vivekananda Global University Jaipur, IndiaMurli ManoharGourDepartment of Mathematics, Vivekananda Global University Jaipur, IndiaSunil DuttPurohitDepartment of HEAS(Mathematics), Rajasthan Technical University, Kota, Rajasthan, IndiaJournal Article20251005Mathematical models are useful for understanding and managing infectious diseases. They assist researchers and public health personnel in decision-making by providing data, evaluating the impact of interventions, and estimating the spread of diseases. The main objective of the present work is to provide an in-depth analysis of the transmission and control of a hepatitis B model under the Caputo fractional derivative, including both qualitative and semi-analytical investigations. Fixed-point theory is employed to establish the conditions for the existence and uniqueness of solutions to the proposed model. The obtained solutions are graphically simulated using MATLAB. The physical significance of this study lies in its ability to capture memory effects and long-term dependencies in the transmission dynamics of the hepatitis B model, which cannot be explained by classical models. The results provide valuable insights for designing effective disease-control strategies and contribute to the advancement of fractional epidemiological modeling, with potential applications in public health policy and clinical research.https://jmm.guilan.ac.ir/article_9544_c4b08c95519ae37bacf33e70b8f8ac88.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Robotic optimization with high-dimensional Pareto front visualization10931105954510.22124/jmm.2026.31644.2849ENArtemMaminovFederal Research Center ``Computer Science and Control'' of the Russian Academy of Sciences (FRC CSC RAS), Moscow, RussiaJournal Article20250909In this paper, we consider an approach for multi-criteria optimization of key design characteristics for robots. We use 5 criteria: Workspace Area, Space Utilization Index, Global Dexterity Index, Global Manipulability Index and Global Resistivity Index. The first two characterize workspace, while the latter three evaluate kinematic performance throughout the workspace. The Pareto-set visualization for such problem can be a challenging task, since the objective space is five-dimensional. We consider clustering approach for efficient reduction of the number of Pareto points. The calculation of the indexes is performed automatically using interval analysis techniques. The experimental validation was performed for three parallel manipulators: 2-RPR, DexTar, PRRRP. We compare the proposed approach with random sampling method and exact Pareto front, calculated with ``brute force'' algorithm.https://jmm.guilan.ac.ir/article_9545_20612cd4b82a496094330a52ce39a5fc.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801A GPU / CPU faster block Arnoldi method for solving large-scale Lyapunov equation11071124955610.22124/jmm.2026.32050.2896ENIliasAbdaouiENSA Oujda, Equipe MSN, Lab. LM2N, Université Mohammed Premier, MoroccoJournal Article20251022Krylov methods have proven effective in solving large-scale matrix equations with sparse coefficients, in particular through the use of the extended Arnoldi process, which involves the inverse of the matrix coefficients in the projection subspace. This approach has significantly reduced the time and number of iterations needed to find a suitable solution. In this paper, we are interested on solving the low-rank Lyapunov equation whether in the continuous or discrete case. We propose to enhance the convergence time by modifying the Block Arnoldi process so that the Krylov projection subspace contains additional blocks from the inverse of the square coefficient of this equation. Our intention is to benefit from these additional informations, similar to the extended Arnoldi version, without incorporating them at each iteration, thus preventing any impact on the convergence speed. To confirm the effectiveness of the proposed method, some numerical results obtained using CPU and GPU implementations are provided.https://jmm.guilan.ac.ir/article_9556_99f9dfb585e35763057ccb4a5890647a.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801A hybrid bi-objective mathematical model for multi-criteria ranking problem of the branches of Sepah bank: an integration of best-worst and SAW approaches11251145956310.22124/jmm.2026.32512.2948ENHamidSoleimanpourDepartment of Financial Management, CT. C., Islamic Azad University, Tehran, IranSadeghNiroomandDepartment of Industrial Engineering, Firouzabad Higher Education Center, Shiraz University of Technology, Shiraz, IranZadollahFathiDepartment of Industrial Engineering, Firouzabad Higher Education Center, Shiraz University of Technology, Shiraz, IranAliMahmoodiradDepartment of Mathematics, Bab. C, Islamic Azad University, Babol, IranJournal Article20260108In this study we consider the multi-criteria ranking problem of the branches of Sepah bank in Fars province of Iran. Compared to literature, a more complete set of criteria are considered to evaluate and rank the bank branches. The data for the last three years of the branches in the criteria are considered to evaluate and rank them. A bi-objective mathematical model is proposed to evaluate the criteria and the bank branches simultaneously. For this aim, for the first time the best-worst method (BWM) and simple additive weighting approach (SAW) are integrated by the proposed mathematical model. By applying the proposed model, the criteria and branches are weighted and ranked simultaneously. In order to solve the proposed bi-objective model, a modification of the fuzzy programming approach called TH approach is applied. Based on the nature of the proposed model and the solution approach and their parameters, several experiments are designed and their results are used for sensitivity analysis purposes. The proposed model and solution approach are highly sensitive to their parameters’ values.https://jmm.guilan.ac.ir/article_9563_488e96d2e40fea8e44adc82fcc211057.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801A study on advanced solutions for fractional integro-differential equations integrating Sawi transform and machine learning techniques11471167957010.22124/jmm.2026.32197.2917ENRaghavendranPrabakaranDepartment of Mathematics, Easwari Engineering College, 18 Bharathi Salai, Ramapuram Chennai-600089, Tamil Nadu, India
Department of Mathematics and Science Education, Faculty of Education, Harran University,
Sanliurfa, TurkeyYaminiParthibanDepartment of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and
Technology, Avadi, Chennai, 600062, Tamil Nadu, IndiaJournal Article20251106In this study, a direct method of fractional calculus approach to particular classes of fractional integro-differential equations is given. The method used reveals a number of interesting results most notably an extension of the familiar classical Frobenius' solution. The investigation is mainly based upon the basic results which are given to determine the fractional integro-differential equations by means of the Sawi transform and some extension coefficients defined from binomial series. Newer techniques for the efficient solution of these equations are also discussed and practical examples are used to demonstrate their use. In addition, we consider using a learning-based approach to improve the computation of our solution and illustrate how data-driven approaches can be used for obtaining approximate solutions in cases where analytical methods are not feasible or not efficient. The findings underscore the efficacy of combining classical and modern approaches in addressing complex fractional integro-differential equations.https://jmm.guilan.ac.ir/article_9570_7a35f0757dacc4dc1422e85c13a0180a.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Solution of time fractional Black-Scholes PDE using fractional order generalized Chelyshkov wavelets11691196958510.22124/jmm.2026.32461.2944ENSufiaSabirDepartment of Mathematics and Computing Technology, National Institute of Technology Patna, Patna, 800005, Bihar, IndiaAyazAhmadDepartment of Mathematics and Computing Technology, National Institute of Technology Patna, Patna, 800005, Bihar, IndiaJournal Article20251205This paper presents an efficient numerical technique for solving the time-fractional Black-Scholes equation, which models the pricing of European options. The proposed method is based on a fractional order generalized Chelyshkov wavelets (FOGCW), a generalized form of classical wavelets. The computation of the Riemann-Liouville fractional integral operator (RLFIO) is a key point of this method. An exact formulation of RLFIO corresponding to FOGCW is obtained. The RLFIO of the traditional Chelyshkov wavelet has been previously obtained through Laplace transform techniques; however, due to the complex structure of the scaling and modulation parameters of generalized fractional order, this technique does not work. In this work, we have utilized the regularized beta function to derive an exact formula for the RLFIO of FOGCW. Several numerical examples are presented to confirm the accuracy and efficiency of the proposed method. Error analysis is also conducted.https://jmm.guilan.ac.ir/article_9585_50e9404676d1f48d8106919efbd95c4f.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14320260801Parameter estimation in SIR epidemic model using dynamic selection preference with adaptive mutation factor enhanced differential evolution11971212959210.22124/jmm.2026.32034.2894ENBakhtawerMajeedDepartment of Computer Science, Faculty of Engineering, Science and Technology at IQRA University, Karachi, PakistanZuhaSoomroDepartment of Computer Science, Faculty of Engineering, Science and Technology, IQRA University Main Campus, Karachi, PakistanMansoorEbrahimDepartment of Computer Science, Faculty of Engineering, Science & Technology, IQRA University, Kaarachi, PakistanJournal Article20251021To understand and manage the spread of infectious diseases in epidemiological models such as the Susceptible-Infected-Recovered (SIR) framework, it is vital to accurately estimate the transmission (β) and recovery (γ) parameters. This study proposes the dynamic selection preference with adaptive mutation factor differential evolution (DSP-AMF-DE) algorithm. The algorithm implements an adaptive mutation factor that dynamically regulates the balance between exploration and exploitation in the population over generations, and dynamic selection preference mechanisms that focus the selection of better candidate solutions and maintain diversity. Seven Pakistani regions covering several epidemic waves over a period of 671 days have been included in a multi-regional dataset. Robustness evaluation for multiple independent runs demonstrate the superiority of the proposed algorithm, which considerably outperforms six competing algorithms.https://jmm.guilan.ac.ir/article_9592_3f9ec2cd6502ab8644b0bd4bcf698ddb.pdf