University of GuilanJournal of Mathematical Modeling2345-394X13320250701Portfolio optimization under regime-switching with market path-dependent returns497518846810.22124/jmm.2025.28912.2571ENRezaKeykhaeiDepartment of Mathematics, Khansar Campus, University of Isfahan, Isfahan, IranJournal Article20241106Asset prices typically follow significant trends influenced by the economic environment or overall investor sentiment. Regime-switching is commonly employed to capture asset price dynamics, as it effectively describes significant trends and reflects the changing correlations of asset returns over various periods. This paper explores multi-period mean-variance portfolio optimization under regime-switching with path-dependent returns. Unlike conventional models, this paper assumes that asset returns depend on the entire path of market states rather than just the current one. Consequently, investors base their decisions on all observed states up to the current moment. Utilizing dynamic programming techniques, we derive the path-dependent optimal portfolio strategy and the mean-variance efficient frontier in closed form. Furthermore, we demonstrate that the results from the traditional regime-switching model,<br />can be viewed as specific cases of our proposed model.https://jmm.guilan.ac.ir/article_8468_e16ed9d640052b643fc1e3aed2ea4a7d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701An approximation technique for a system of time-fractional differential equations arising in population dynamics519531847010.22124/jmm.2025.28718.2548ENJugalMohapatraDepartment of Mathematics, National Institute of Technology Rourkela, IndiaSiba PrasadMohapatraDepartment of Mathematics, Konark Institute of Science and Technology, IndiaAnasuyaNathDepartment of Mathematics, Utkal University, Bhubaneswar, IndiaJournal Article20241016In this work, we develop and analyze an approximation technique for the system of time-fractional nonlinear differential equations arising in population dynamics. The fractional of order $ \sigma\in(0,1) $ is taken in the Caputo sense. The proposed technique uses L1 discretization on the uniform mesh to approximate the differential operator. The fractional model is transformed into a system of nonlinear algebraic equations. The generalized Newton-Raphson method is employed to solve the corresponding nonlinear system. A rigorous error estimation is presented. It is shown that the proposed scheme achieved $ (2-\sigma) $ order of accuracy. Lastly, numerical experiment is conducted to demonstrate the validity of the proposed technique.https://jmm.guilan.ac.ir/article_8470_5d72461a5b07dabcf11b79c305d43fe0.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701A new bilevel optimization problem for the image restoration533552854510.22124/jmm.2025.28007.2482ENAbdelmajidEl MourabitMIMSC, EST d'Essaouira, Université Cadi Ayyad, MoroccoIdrissEl MourabitMIMSC, EST d'Essaouira, Université Cadi Ayyad, MoroccoJournal Article20240807This paper presents a novel bilevel optimization approach for a nonlinear partial differential equation. The approach aims to enhance the quality of image denoising by estimating certain parameters within this equation. Our work deals with both analytical and numerical results. Analytically, we establish the existence of a solution to the bilevel optimization problem and apply the Alternating Direction Method of Multipliers algorithm to approximate this solution. Furthermore, the method fine-tunes the restoration process, effectively reducing noise while preserving crucial image features. Finally, numerical results validate the performance of our method, surpassing traditional denoising approaches. This research makes an important contribution to image restoration, paving the way for high-quality practical applications.https://jmm.guilan.ac.ir/article_8545_f6f4a59f5c6aa7453bc6488f04c88b12.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701An iterative method based on Simpson's $3/8$ rule to solve absolute value equations553562854610.22124/jmm.2025.28919.2572ENFarzadRahpeymaiiDepartment of Mathematics, National University of Skills (NUS), Tehran, IranMajidRostamiDepartment of Mathematics, National University of Skills (NUS), Tehran, IranJournal Article20241107Newton's method is one of the important algorithms for solving absolute value equations. In this paper, we introduce an efficient two-step iterative method to improve the Newton algorithm. The new method adopts the predictor-corrector technique in which the first step is generalized Newton method and the second step is based on Simpson's $3/8$ rule.<br />Under some standard assumptions, the convergence of new method and its linear convergence rate are obtained. Numerical results show that the our method is efficient and robust to solve absolute value equations.https://jmm.guilan.ac.ir/article_8546_65131e3e63e05cd147c1f6b343e73588.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701An analytical representation of bivariate isotropic stable density563572865410.22124/jmm.2025.28746.2649ENHosseinKazemzadeh GharechopoghFaculty of Mathematics and Computer Science, Amirkabir University of TechnologyAdelMohammadpourFaculty of Mathematics and Computer Science, Amirkabir University of TechnologyJournal Article20250129Stable random vectors are characterized by their characteristic functions. The multivariate<br /> stable density and distribution functions generally do not have an analytic form. A few numerical<br /> methods have been developed to compute density functions of parametric stable random vectors.<br /> However, they have some limitations in terms of the range of the tail index. In this work, via the<br /> inversion formula, we present a new analytical representation of the density function of a bivariate<br /> isotropic stable random vector. We show that the analytical representation can be reduced to a closed<br /> form at the origin.https://jmm.guilan.ac.ir/article_8654_40a2c66ed965e94bae14b16eef77e7d5.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701An iterative method for solving the generalized total least squares problem573592858710.22124/jmm.2025.28866.2568ENSaeedKarimiDepartment of Mathematics, College of Sciences, Shiraz University, Shiraz 7187919556, Iran & Department of Mathematics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf
University, Bushehr, IranBentelhodaZaliDepartment of Mathematics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf
University, Bushehr, IranJournal Article20241102This paper introduces a novel method for solving the generalized total least squares problem, an extension of the total least squares problem. The generalized total least squares problem emerges when solving overdetermined linear systems with the multiple right-hand sides $\mathbf{AX} \thickapprox \mathbf{B}$, where both the observation matrix $\mathbf{B}$ and the data matrix $\mathbf{A}$ contain errors. Our approach involves extending the Taylor series expansion to reformulate the generalized total least squares problem into a linear problem, allowing us to employ the tensor form of the generalized least squares algorithm for efficient computation. This technique streamlines the computational process and enhances solution accuracy. For a more detailed survey, we compare the proposed method for solving the generalized total least squares problem with one of the matrix format methods for the associated total least squares problem. Empirical results show that our method significantly improves computational efficiency and solution precision. Additionally, we demonstrate its practical application in the context of image blurring.https://jmm.guilan.ac.ir/article_8587_c5103a8c379aeaff20100f93d1e54904.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701Non-classical sinc collocation method for approximating Hallen's integral equation593608858910.22124/jmm.2025.28972.2578ENRozhanMahamad HajiDepartment of Mathematics, Faculty of Sciences, University of Kurdistan, Sanandaj, Kurdistan, IranAmjadAlipanahDepartment of Mathematics, Faculty of Sciences, University of Kurdistan, Sanandaj, Kurdistan, IranJournal Article20241117In this paper, we propose a novel numerical method for solving Hallen’s integral equation, based on the sinc collocation approximation. The key innovation of our approach lies in the incorporation of weight functions into the traditional sinc-expansion framework. By leveraging the properties of sinc collocation, we transform Hallen’s integral equation into a system of algebraic equations, which can be solved efficiently. Our method involves discretizing the singular kernel of Hallen’s integral equation and then applying the sinc approximation. Additionally, we provide a detailed analysis of the convergence and error estimation of the proposed method. Numerical results are presented for three distinct values of $\lambda$ and $l$, as well as for three different weight functions: $w(t)=1+\sin(\pi t)$, $w(t)=1+\cos(\frac{\pi t}{2})$ and $w(t)=1+t$.https://jmm.guilan.ac.ir/article_8589_c5b8716617b3fd1293ae94b7925b49d4.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701Comparative study of numerical methods for singularly perturbed boundary turning point problems with mixed boundary conditions609628860010.22124/jmm.2025.28691.2547ENJanani JayalakshmiGPG and Research Department of Mathematics, Seethalakshmi Ramaswami College( Affiliated to Bharathidasan University), Tiruchirapalli-2, Tamilnadu, IndiaSekarElangoAmrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore, Tamilnadu, IndiaRajaVelusamyDepartment of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu, Tamilnadu IndiaTamilselvanADepartment of Mathematics, Bharathidasan University, Tiruchirappalli, IndiaJournal Article20241015A comparative study on numerical methods for Singularly Perturbed Boundary Turning Point Problems (SPBTPPs) featuring discontinuous source terms are examined. The study involves developing and analyzing two specific numerical techniques: the finite difference method and a hybrid difference method incorporating a Shishkin-type mesh. This approach demonstrates notable capabilities, exhibiting almost first-order and second-order convergence for the finite difference and hybrid difference methods, respectively. Numerical results are given to support the theoretical findings.https://jmm.guilan.ac.ir/article_8600_694006fcac750f2568cf7fc1f5d2128e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701A novel and efficient operational matrix method for solving multi-term variable-order fractional differential equations629644865310.22124/jmm.2025.29744.2655ENTaherehEftekhariYau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, ChinaJalilRashidiniaSchool of Mathematics and Computer Science, Iran University of Science and Technology (IUST), Tehran, 16846 13114, IranJournal Article20250203The main aim of this research is to present a novel and efficient method based on the Müntz-Legendre polynomials for solving differential equations involving variable-order fractional Caputo derivatives. For the first time, based on the M$\rm{\ddot{u}}$ntz-Legendre polynomials, a formula for the operational matrix of the variable-order fractional Caputo differential operator is derived. By using this operational matrix via the collocation method, we convert the proposed problem into a system of equations. Then, we solve the obtained system by the Newton method to provide an approximate solution for the problem. Furthermore, we obtain an error bound for the approximation. Finally, we solve four test problems to confirm the reliability and effectiveness of the proposed method.https://jmm.guilan.ac.ir/article_8653_8285b384c0254d98a43ed676665c3a5e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701On recovering space-dependent source term in a degenerate nonlocal parabolic equation645662865510.22124/jmm.2025.29151.2596ENMarouaNouarICOSI laboratory, Department of Mathematics, Khenchela University, Khenchela, AlgeriaAbdeldjalilChattouhICOSI laboratory, Department of Mathematics, Khenchela University, Khenchela, AlgeriaJournal Article20241204Identifying the unknown source terms in diffusion models, including nonlocal ones, is an active research area with significant applications in engineering and scientific fields such as population dynamics, biology, and physics. This study examines an inverse problem focused on recovering a space-dependent source term in a degenerate diffusion model that includes a nonlocal space term, using final-time measured data. As a first step, the inverse problem is reformulated as an optimization one by considering its solution as the minimizer of a well-defined objective function. The existence of a unique solution to the associated direct problem is discussed in a functional framework based on suitable weighted Sobolev spaces. After that, we prove the existence of a minimizer by means of standard arguments, and establish a first-order necessary optimality condition. Using this last one, we obtain some results concerning the stability and local uniqueness property. For the numerical reconstruction of the missing source term, we designed an algorithm based on the Landweber iterative method and showed its effectiveness by providing several numerical tests.https://jmm.guilan.ac.ir/article_8655_32cd16ac18e5d7f44213f78adbe736a4.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701On $q$-fractional differential problem with parameter and $q$-derivative boundary conditions663674865810.22124/jmm.2025.26666.2359ENAbdolaliNeamatyDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranFatemeShahabiDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranJournal Article20240422In this paper, we study the existence of a positive solution for $q$-fractional boundary value problem by employing the fixed-point theorem. Our analysis relies on the Banach space and the fixed point theorem. Finally, we provide an example to verify our hypothesis and showcase our results.https://jmm.guilan.ac.ir/article_8658_cdce42a995a5fc70bb1b4c25627b45eb.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701A study on the existence results for neutral functional random integro-differential equations with infinite delay675693865910.22124/jmm.2025.27789.2447ENSrinivasanMadhumithaDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R
& D Institute of Science and Technology, Chennai - 600062, Tamil Nadu, IndiaGunasekarTharmalingamDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai - 600062, Tamil Nadu, India &
School of Artificial Intelligence and Data Science, Indian Institute of Technology (IIT), Jodhpur 342030, IndiaPrabakaranRaghavendranDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Chennai - 600062, Tamil Nadu, IndiaShyamSundar SantraDepartment of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, IndiaSamadNoeiaghdamInstitute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, ChinaJournal Article20240627This study investigates the solutions of neutral functional integro-differential equations and second order neutral functional differential equations with delays and random effects. The Kakutani fixed-point theorem is used to prove the existence of mildly random solutions in the stochastic domain and to launch this investigation. The research heavily relies on core notions from functional analysis, and to make these concepts clearer, an explicit case is given.https://jmm.guilan.ac.ir/article_8659_ee3be544be6db23e6d94ab7043bee472.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701Fractal complex analysis695704869210.22124/jmm.2025.29566.2629ENAlirezaKhalili GolmankhanehDepartment of Physics, Ur.C., Islamic Azad University, Urmia 63896, West Azerbaijan, Iran,
& Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080-Campus, Van,
TurkeyRosanaRodríguez-LópezDepartamento de Estatística,
Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 10587, Spain0000-0001-5852-9845IvankaM. StamovaDepartment of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USAErcanÇelikDepartment of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Bishkek,
KyrgyzstanJournal Article20250114In this paper, we begin by providing a concise overview of fractal calculus. We then explore the concepts of fractal complex numbers and functions, define the fractal complex derivative, and derive the fractal Cauchy-Riemann equations. dditionally, we introduce fractal contour integrals, offer illustrative examples, and present their visualizations. Finally, we examine and visualize the transformations of circles under fractal complex functions.https://jmm.guilan.ac.ir/article_8692_de388dde01a6fcf67ed6d86914b5cec6.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701Evaluation of decision-making units using directional distance function with weak disposability in the presence of undesirable outputs705724872910.22124/jmm.2025.29485.2620ENJafarPourmahmoudDepartment of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranSamanehRadfarDepartment of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranJournal Article20250105This study evaluates decision-making units (DMUs) that produce unavoidable undesirable outputs, which negatively affect performance. Previous studies by researchers have explored approaches for calculating the minimum undesirable outputs, presenting the abatement range for undesirable outputs and assessing DMU efficiency, yet challenges remain. To address this, we introduce a new method based on the directional distance function model with individual-proportion weak disposability. The proposed method calculates the minimum unavoidable undesirable outputs, evaluates DMU efficiency for both undesirable and minimum undesirable outputs, separates the effects of desirable and undesirable outputs on inefficiency, and resolves the limitations of earlier methods. Finally, the proposed method is applied to practical examples to demonstrate its superiority over existing approaches. https://jmm.guilan.ac.ir/article_8729_2c3d134e8519b9c47ec0f73b9b1bc173.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X13320250701Atangana–Baleanu–Caputo (ABC), Caputo-Fabrizio (CF), and Caputo fractional derivative approaches in fuzzy time fractional cancer tumor growth models725746874410.22124/jmm.2025.29638.2640ENAmandeepSinghDepartment of Mathematics, Panjab University, Chandigarh, India & Department of Mathematics, Government College Gurdaspur, Punjab, IndiaSaritaPippalDepartment of Mathematics, Panjab University, Chandigarh, IndiaJasmineSatiCentre for Nuclear Medicine, Panjab University Chandigarh, IndiaJournal Article20250123This article introduces a new approach for solving a time-fractional cancer tumor model using Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu-Caputo (ABC) fractional derivatives, accounting for varying net-killing rates of cancer cells in an uncertain environment. The model with the Caputo derivative is initially tackled using an explicit finite difference method (EFDM) with a fully time-dependent net killing rate. Approximate solutions for two different net death rates are obtained using the Sumudu transformation (ST) combined with the Adomian decomposition method (ADM), providing more accurate approximations than the EFDM. The model's behavior is analyzed with 2D and 3D visualizations. Convergence and error analysis of the method for the Caputo fractional derivative have been performed. The ADM provides reliable approximations for fractional models with fuzzy parameters, outperforming the EFDM by achieving lower absolute errors. The results exhibit symmetric lower and upper approximations around zero, effectively capturing the fuzzy nature of the solution. All methods converge to zero at higher cuts in fuzzy triangular numbers, i.e. \( v = 1 \).https://jmm.guilan.ac.ir/article_8744_7a0ef50d9a2a15529a03f49e9aff6cfe.pdf