University of GuilanJournal of Mathematical Modeling2345-394X14220260501A gradient projection method for solving nonlinear optimal control problems with time-varying delays363378900210.22124/jmm.2025.30121.2691ENSeyed MojtabaMeshkaniDepartment of Mathematics, Payame Noor University, 19395-4697, Tehran, IranSohrabEffatiDepartment of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, IranAghilehHeydariDepartment of Mathematics, Payame Noor University, 19395-4697, Tehran, IranJournal Article20250405An effective numerical method using gradient projection is proposed for solving an optimal control problems that involve time-varying delays in control and state variables. First, a variational inequality is established as necessary conditions. The main idea in variational inequality is to compute the gradient of the objective functional, taking into account time-dependent delays in control and state variables. Then, an iterative scheme utilizing a projection operator is presented, followed by a convergence analysis of the method for a coercive objective functional. At the end, several examples are provided to illustrate that the theoretical finding is efficient.https://jmm.guilan.ac.ir/article_9002_88fdaf2f039648457e05a8b34416b31d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501A robust fitted finite difference method for semi-linear two-parameter singularly perturbed PDEs379405919610.22124/jmm.2025.30916.2776ENMekashaw AliMohyeDepartment of Mathematics, College of Natural and Computational Science, Wolkite University, Wolkite, EthiopiaJustin B.MunyakaziDepartment of Mathematics and Applied Mathematics University of Western CapeTekle GemechuDinkaDepartment of Applied Mathematics Adama Science and Technology UniversityYusuf HussenHajiDepartment of Mathematics, Arsi University, Asela, EthiopiaAbe NUraWareDepartment of Mathematics, Arsi University, Asela, EthiopiaJemal MuhammedAhmedDepartment of Mathematics, Oda Bultum University, Chiro, EthiopiaJournal Article20250609In this article, a new numerical approach is developed for nonlinear two-parameter singularly perturbed initial-boundary value problems. The implicit backward Euler discretization for the time derivative and the fitted operator technique in the spatial domain are employed. Newton's quasilinearization technique is applied to the nonlinear terms. An investigation of parameter-uniform error estimates shows that the developed approach is first-order accurate in both time and space. However, a temporal mesh refinement technique is introduced to improve the order of accuracy to two. Two examples are provided and implemented in Python to validate the applicability of the method, and the results are displayed in tables and graphs.https://jmm.guilan.ac.ir/article_9196_a1da3bcb9a2e740a13facab78cc434d7.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Modeling and analysis of deforestation and pollution dynamics induced by industrialization using the fractal-fractional Atangana-Baleanu derivative407430919810.22124/jmm.2025.31414.2822ENNobinDaimaryGauhati University, Assam, IndiaRanuPaulGauhati University, Assam, India0009-0007-1614-3072Journal Article20250815This study presents a fractal-fractional model in the Atangana–Baleanu sense to investigate the dynamics of deforestation and pollution driven by industrialization. The model is analyzed for positivity and boundedness, and the existence and uniqueness of its solution are established using fixed-point theory. The system’s equilibrium points are identified, and the threshold parameter <br />$\mathfrak{R_0}$ is determined, with local asymptotic stability confirmed for all equilibria. Sensitivity analysis highlights the key parameters influencing $\mathfrak{R_0}$, while Ulam–Hyers stability ensures robustness of the solution. Lagrangian polynomial interpolation is employed to approximate the solution, and phase portraits along with numerical simulations in Matlab illustrate the model’s dynamic behavior. The results demonstrate that the fractal-fractional approach provides a comprehensive framework for capturing complex environmental interactions, offering valuable insights into the effects of industrialization on deforestation and pollution.https://jmm.guilan.ac.ir/article_9198_9e76332a786da2f23b55998d929a734e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Hunting cooperation in prey-predator models: spatiotemporal patterns and bifurcation analysis with holling type IV response431451920110.22124/jmm.2025.31303.2805ENAtish KumarSethyCentral University of Odisha, Koraput, Sunabeda N.A.D Post Office, 763004
Department of MathematicsJyotiskaDattaCentral University of Odisha, Koraput, Sunabeda N.A.D Post Office, 763004
Department of MathematicsJournal Article20250730This study examines a class of predator models that incorporate cooperative predation within<br />specialized carnivore populations. The functional response is parameterized, and numerical simulations are employed to support the analytical investigation of pattern formation potential. The principal finding of this work is that stable Turing patterns, such as stripes, can emerge when predator distributions are more localized than those of their prey. Specialized predator groups that cooperate in hunting contribute to the formation of prey aggregation zones (roost patches), as cooperation enhances predation efficiency. The results demonstrate that although predators exhibit limited mobility, cooperative behavior during hunting promotes both successful predation and long-term coexistence with prey populations.https://jmm.guilan.ac.ir/article_9201_97e708fda3802908678f57fe0726a202.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Higher order numerical method for a class of singularly perturbed time dependent nonlinear reaction diffusion problems453470921510.22124/jmm.2025.31159.2791ENManikandanMariappanDepartment of Mathematics, School of Engineering, Presidency University, Bengaluru - 560 064, Karnataka, IndiaJournal Article20250712Nonlinear science plays an important role in modern technology. Because of the limitations over the linear theories and the chaotic nature of the problems in this technological era, investigation of nonlinear problems has become indispensable to analyse the dynamics of complicated and multi scale characteristics problems. This article aims at the analysis and implementation of a numerical method for a class of singularly perturbed time dependent nonlinear reaction diffusion problems. Together with classical finite difference operators, a piecewise uniform Shishkin mesh in the spatial direction and a uniform mesh in the temporal direction are used to formulate a new numerical method to solve the class of problems. The method is proved to be second order convergent in space and first order convergent in time uniformly with respect to the perturbation parameter. Numerical experiments are included which support the theoretical results.https://jmm.guilan.ac.ir/article_9215_64aae1dffcb8073d33edc7f4919f6ffc.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Convex optimization approach for the path-following problem of two collaborative robots471487922210.22124/jmm.2025.31212.2798ENMaryamKia-LashgamiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of
Guilan, Rasht, Iran.MohammadKeyanpourDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
University of Guilan, P.O. Box 1914, Rasht, Iran.Journal Article20250719This paper investigates the time-optimal path-tracking problem for a collaborative robotic system, considering some limitations and dynamic characteristics. This problem is formulated for a robotic system consisting of two-link planar manipulators with and without bar cases along a predetermined geometric path in minimum time. The main challenges are to satisfy both the co-position and co-time conditions of the end-effector movement, as well as the physical limitations of the applied torque to the joints. Through discretization and convexification, we convert the problem into a convex cone optimization problem. The numerical example confirms the effectiveness of the method.https://jmm.guilan.ac.ir/article_9222_b482a06a3e5d0e335f0284dbeb87add2.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Mittag-Leffler wavelet-based numerical method for fractional pantograph delay differential equations489508923310.22124/jmm.2025.31321.2807ENArezooGhasempourDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranYadollahOrdokhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranMohsenRazzaghiDepartment of Mathematics and Statistics, Mississippi State University, MS, USAJournal Article20250804This paper proposes a robust numerical framework for solving fractional pantograph delay differential equations. The approach leverages the Riemann–Liouville fractional integral operator, represented through Mittag-Leffler wavelet functions within a collocation-based scheme. To facilitate computation, an operational matrix is constructed, enabling the transformation of the fractional differential system into a system of algebraic equations. The proposed method’s accuracy, stability, and convergence are rigorously validated through comprehensive numerical experiments.https://jmm.guilan.ac.ir/article_9233_c9128f6e51cdf96bde74edba9cb69641.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501An accelerated method for solving constrained multi-objective optimization509532924010.22124/jmm.2025.30721.2753ENNiloofarSalehi MokariDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranHadiBasirzadehDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, IranVahidMorovatiDepartment of Mathematics, University of Hormozgan, Bandarabbas, IranJournal Article20250520A novel non-parametric algorithm is introduced for solving constrained multi-objective optimization problems. At each iteration, a convex sub-problem is solved to determine the search direction, while a non-monotone line search technique is used to determine the step size. An adaptive acceleration term, computed from changes in the search directions, is incorporated to scale the step and dynamically enhance convergence performance. The algorithm’s effectiveness relies on a diverse set of initial feasible solutions to accurately approximate the non-dominated boundary. Benchmark tests validate the approach, with Pareto fronts compared to those obtained using the Zoutendijk method. Numerical evaluations demonstrate superior performance in terms of convergence rate and solution quality. The algorithm is also applied to a real-world engineering design problem involving speed reduction, highlighting its computational efficiency and robustness in practical applications.https://jmm.guilan.ac.ir/article_9240_6325aaf7c4dccebd2cd9ddacf487bb28.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501The method based on quintic B-spline functions for addressing time-fractional advection-dispersion equations533556924310.22124/jmm.2025.31501.2833ENMohamedAdelDepartment of Mathematics, Faculty of Science, Islamic University of Madinah,
Medina, KSA.SomayiehAbdi-mazraehDepartment of Applied Mathematics, Faculty of Mathematics, Statistics and
Computer Sciences,
University of Tabriz, Tabriz, IranGolamrezaZakiDepartment of Applied Mathematics, Faculty of Mathematics, Statistics and
Computer Sciences,
University of Tabriz, Tabriz, IranSafarIrandust-PakchinDepartment of MathematicsJournal Article20250825This paper introduces a numerical method designed to address the fractional time advection-dispersion equation. Initially, the time dimension is discretized by employing the L1 method. Subsequently, quintic B-spline functions are utilized for the discretization of the spatial dimension. This <br />approach yields a system of algebraic equations that can be efficiently solved. The proposed method is proven to be unconditionally stable. Numerical experiments provide compelling evidence of the method’s efficiency and effectivenesshttps://jmm.guilan.ac.ir/article_9243_9250861472f7a03bbcd991807a6d0570.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Numerical pricing of American options under a nonlinear Black-Scholes framework with mixed fractional Brownian motion557577924510.22124/jmm.2025.30891.2773ENAfshinBabaeiFaculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran.MaryamRezaeiFaculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.Journal Article20250605Transaction costs significantly impact option pricing and trading strategies in financial markets. This study investigates the valuation of American options under transaction costs, modeled as a linear function of the underlying asset price. To capture long-range dependence in asset returns, the underlying dynamics are described by a mixed fractional Brownian motion (fBm). The model incorporates dividend-paying stocks, along with time-varying interest and dividend rates. A compact finite difference scheme is developed to solve the resulting nonlinear Black-Scholes equation, ensuring numerical stability and accuracy. The proposed framework offers an efficient approach for pricing American options in realistic market conditions.https://jmm.guilan.ac.ir/article_9245_9a406f97ece14eddc4d6d2bf17bca9b5.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Blood flow through a stenosed artery under MHD two-phase conditions with Hall effect, radiation and diffusion579594924710.22124/jmm.2025.31551.2840ENSurendra KumarAgarwalIIS Deemed to be University, Jaipur
MANSAROVARGauriSethiDepartment of Mathematics IIS Deemed to be University Jaipur RajasthanAsthaPareekIIS Deemed to be University, Jaipur
MANSAROVARJournal Article20250901This study investigates the combined effects of heat and mass transfer on two-phase blood flow through a stenosed artery, considering the influence of the Hall current. Blood is modeled as a Newtonian fluid in both the central core and plasma regions. A system of differential equations governing momentum, temperature, and concentration is developed separately for each region. The analysis incorporates magnetic field, thermal radiation, and Hall current effects. Key flow characteristics, including flow resistance, total volumetric flow rate, and wall shear stress, are evaluated for varying magnetic field strengths, radiation parameters, and Hall current intensities. The findings indicate that stronger magnetic fields and radiation levels lead to a reduction in blood flow velocity and temperature. The inclusion of the Hall current introduces a cross-flow component due to the induced electric field, further modifying the velocity distribution, particularly in the plasma region. Moreover, an increase in the Schmidt number enhances the concentration profiles in both the core and plasma regions. Overall, the Hall effect significantly alters the magnetic interaction with the flow, impacting the distribution of mechanical and thermal quantities throughout the arterial segment. The results have potential biomedical applications in magnetic resonance imaging (MRI), targeted drug delivery, and electromagnetic therapy, where controlled magnetic and electric fields influence blood flow and heat transfer in vascular systems.https://jmm.guilan.ac.ir/article_9247_d446f8e6bed93c2cb19b1f055ee8aa10.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501A fast and cheap approach for strengthening Lagrangian bound for the generalized Celis-Dennis-Tapia subproblem595608926410.22124/jmm.2025.31942.2884ENTemadher AlassiryAlmaadeedQatar University-College of Arts and Sciences-Dept Mathematics and Statistics, P.O. Box 2713
Qatar University, Doha- QatarAbdelouahedHamdiQatar University-College of Arts and Sciences-Dept Mathematics and Statistics, P.O. Box 2713, Qatar University, Doha- QatarAkramTaatiFaculty of Mathematical Sciences, University of Guilan, Rasht, Iran.Journal Article20251011In this paper, we consider the generalized Celis-Dennis-Tapia problem<br />which is the problem of minimizing a nonconvex quadratic function subject to<br />two quadratic inequality constraints, one of which being convex. When there is<br />a positive duality gap, by exploiting an equivalent form of the dual Lagrangian<br />problem, we propose to improve the dual bound by adding one or two linear cuts<br />to the Lagrangian relaxation. The present work is motivated by and generalizes<br />the results of [14] for the problem with two strictly convex quadratic constraints.<br />Our main contribution is to show that one can include the feasible region in a con-<br />vex set and then follow the approach in [14] to construct the linear cuts based on<br />supporting hyperplanes of the convex set. Numerical experiments are conducted<br />to assess the quality of the proposed bounds.https://jmm.guilan.ac.ir/article_9264_3bb0c7a429b19885a3efa780276fd8df.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Mathematical model and hybrid meta-heuristic solution approaches for hub location problem with hybrid drone-airplane delivery mode609646926910.22124/jmm.2025.31720.2857ENMehrnazMohebbiShiraz University of TechnologyHamid RezaMalekiFaculty of Mathematics, Shiraz University of Technology, Shiraz, IranSadeghNiroomandShiraz University of TechnologyJournal Article20250919This study addresses the integrated hub location and drone delivery problem, an area with few5<br />prior investigations. We propose a bi-objective integer linear programming model to minimize total cost and total drone route time. A novel three-zone structure allows drone transfers between zones via cargo planes, enhancing realism and complexity. Drone capacities are categorized as light and heavy, improving allocation flexibility. Due to the model’s complexity, several metaheuristic algorithms including Genetic Algorithm, Differential Evolution, Simulated Annealing, and their hybrid versions (SA-GA and SA-DE) are developed and compared. Parameter tuning is performed using the Taguchi method. Computational experiments on various instances show that hybrid algorithms outperform classical methods and scale effectively for larger problems, providing a practical and integrated framework for hub location and drone delivery planning.https://jmm.guilan.ac.ir/article_9269_5940ad57fb95609dea042874deb754db.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Two-stage multi-objective technology portfolio planning under resource constraints (case study: Iranian technology development fund)645671928910.22124/jmm.2025.31547.2839ENMarziehShaverdiDepartment of STI Financing and Economics,
National Research Institution for Science Policy (NRISP), Tehran, Iran.KhaterehGhorbani-MoghadamMosaheb Institute of MathematicsJournal Article20250901This study proposes a novel two-stage multi-objective framework for optimal technology portfolio planning and resource allocation under constraints, specifically for Technology Development Funds (TDFs). The integrated methodology combines the Analytic Network Process (ANP) for prioritizing strategic technology fields with a multi-period Mixed-Integer Linear Programming (MILP) model, solved using a Revised Multi-Choice Goal Programming (RMCGP) approach. The model’s objectives are to maximize technological export potential, maximize international technological cooperation, and minimize financial risk, while incorporating critical real-world mechanisms such as staged financing contingent on Technology Readiness Level (TRL) progress, loan moratorium, and repayment periods.<br />The framework was validated through a real-world case study of an Iranian Technology Development Fund (ITDF), involving eight technology fields and up to 30 projects per field. Key quantitative results demonstrate the model’s efficacy: by reducing the risk objective’s weight from 0.3 to 0.1, the number of approved projects increased over fivefold (from 12 to 65), and the total allocated resources surged nearly tenfold (from $22.2 million to $217.5 million). Sensitivity analysis revealed that fields with high export potential and collaboration capacity (e.g., Advanced Machinery) received the highest funding, while the staged financing mechanism successfully identified and terminated 25% of projects for insufficient technical progress after the first stage. The proposed model provides a robust decision-support tool for policymakers to enhance the strategic impact and financial efficiency of national technology investments.https://jmm.guilan.ac.ir/article_9289_c5c9c33fed7df383c3c4c61b0fe3db6b.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Full and partial controllability of the Kermack-Mckendrick system with time- varying incidence rates673697929510.22124/jmm.2025.31390.2818ENHamzaEl MahjourMASI research Team
Department of Information Systems and Communication
ENSAT, Abdelmalek Esaadi University, MoroccoAadilLahrouzLAM research laboratory
Department of Mathematics
FSTT, Abdelmalek Essaadi UniversityOmarZakaryStatistics and Modelling research team
Department of Mathematics
FSBM, University of Hassan IIMariamRedouaneLAM research laboratory
Department of Mathematics
FSTT, Abdelmalek Essaadi UniversityJournal Article20250812This study contributes to epidemic control literature by introducing a time-varying inci-<br />dence rate and establishing global controllability of the nonlinear SIR system, offering a<br />practical framework for adaptive control strategies. We derive explicit solutions for partial<br />controllability, demonstrating the feasibility of controlling the infected population, pro-<br />viding guidance for outbreak management. Numerical methods exploiting an algorithmic<br />approach achieve full control, targeting a desired state (Sd, Id). A novel hybrid method<br />integrates analytical solutions with algorithmic optimization, leveraging explicit expres-<br />sions for I(t) and S(t) to enhance precision and efficiency of epidemic control strategies,<br />advancing adaptive management approacheshttps://jmm.guilan.ac.ir/article_9295_fd6f0670afa9641d22cff7f55adf61dd.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Dual analysis of myocardial infarction using fractional mathematical modeling and machine learning699722929910.22124/jmm.2025.31534.2837ENTharmalingamGunasekarDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\&D Institute of Science and Technology, Chennai - 600062, Tamil Nadu, IndiaSumaiyaBanuDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\&D Institute of Science and Technology, Chennai - 600062, Tamil Nadu, IndiaShyam SundarSantraJIS College of Engineering, Kalyani, Nadia, West BengalDumitruBaleanuDepartment of Computer Science and Mathematics, Lebanese American University, Beirut - 11022801, LebanonJournal Article20250830This paper presents a novel fractional-order mathematical model of myocardial infarction in women who are users of combined oral contraceptive pill and who also develop comorbidity due to various reasons. The system of equations incorporate Caputo fractional derivative to capture memory effects of the model. Existence and uniqueness of solution of the mathematical model is derived. Numerical simulations were rigorously conducted on the math model with varying fractional order namely, $0.3$, $0.5$ and $0.8$ using Euler's method. The numerical results thus obtained are simulated by Adam's method for 200 days period. The output from these simulations form the dataset of the Bayesian regularization neural network (BRNN) with dataset split for training, testing and validatating the computational model. Bayesian regularization is incorporated to handle overfitting efficiently. Root Mean Square Error (RMSE) are computed for all three fractional orders respectively. Regression analysis is conducted which yielded perfect correlation \((R=1)\) accross the all datasets. The combined mathematical and computational analysis form a strong layout in myocardial infarction risk prediction, diagnosis and treatment in young women.https://jmm.guilan.ac.ir/article_9299_6593aeb65997ccb0968e730a257ed0b3.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Classification of flow behavior near generalized equilibrium points in piecewise smooth systems723739930110.22124/jmm.2025.30519.2738ENZohrehZareiDepartment of Math., University of Hormozgan, Bandar Abbas, IranMajidKarimi AmalehDepartment of Math, University of Hormozgan, Bandar Abbas, IranJournal Article20250601The aim of this paper is to classify the various states of flow behavior for piecewise smooth systems near generalized equilibrium points. Seven categories are introduced based on the sign of the vector field across the discontinuity boundary, each encompassing distinct dynamical configurations. We investigate how a small perturbation parameter $\mu$ influences the existence, type, and stability of generalized singular points in planar piecewise linear systems. Starting with a one-dimensional example to illustrate core mechanisms, we extend the analysis to two dimensions, providing a detailed classification grounded in the signs of the system’s components. Our results yield a comprehensive framework for understanding how generalized singular points govern local dynamics, including bifurcations induced by parameter variation. This work contributes to the theoretical foundation for analyzing discontinuity-induced phenomena such as sliding modes and non-smooth bifurcations.https://jmm.guilan.ac.ir/article_9301_fe3017a88aba3c657d183b055fb140ae.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Dynamical analysis of novel minimal SEIR model incorporating asymptomatic transmission741760930210.22124/jmm.2025.31474.2832ENViralkumar D.PatelDepartment of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat, India.
Department of Mathematics, Shri Alpesh N. Patel Post Graduate Institute of Science & Research, Anand.Abdulvahid H.HasmaniDepartment of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India.Journal Article20250825We propose a modified SEIR model that includes asymptomatic transmission directly in the infection term, avoiding the need for a separate asymptomatic compartment while keeping the model realistic. The basic reproduction number ($\mathcal{R}_0$) is calculated to measure the potential for disease spread. Local stability analysis shows that the disease-free equilibrium is stable when $\mathcal{R}_0 < 1$ and unstable when $\mathcal{R}_0 > 1$, while the endemic equilibrium is locally stable in the latter case. A forward bifurcation at $\mathcal{R}_0 = 1$ is identified, indicating a smooth transition from the disease-free equilibrium to a unique endemic equilibrium without coexistence of the two equilibria. Global stability results show that the disease-free state is globally asymptotically stable for $\mathcal{R}_0 \leq 1$, and the endemic state is globally asymptotically stable for $\mathcal{R}_0 > 1$. Simulations using early COVID‑19 data support these findings, showing that higher asymptomatic transmission prolongs outbreaks, increases peaks, and delays elimination. Evaluation of control strategies reveals that isolation is more effective than testing alone, and their combination produces the greatest overall reduction in disease spread under appropriate assumptions.https://jmm.guilan.ac.ir/article_9302_30a58393c2cfbe438486b4983c339a78.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Novel Legendre-Jaiswal functions for solving time-space fractional partial differential equations761786930510.22124/jmm.2025.31438.2827ENSantoshiTareiDepartment of Mathematics
National Institute of Technology RourkelaAnkurKanaujiyaDepartment of Mathematics, NIT Rourkela, Odisha, IndiaJournal Article20250818This paper examines a new fractional function based on Legendre and Jaiswal polynomials to solve linear and nonlinear time-space fractional partial differential equations of linear and nonlinear class. The Caputo sense is applied while using the fractional derivative. These problems can be solved using the collocation method, operational, and pseudo-operational matrices of integer and fractional-order integration. Using operational matrices, pseudo-operational matrices, and the collocation method, the problem is transformed into a system of algebraic equations. An upper bound on the error of the fractional-order integral operational matrix is computed. Furthermore, a detailed stability and convergence analysis of the collocation scheme presented to validate the robustness of the numerical approach. The applicability and effectiveness of the approach are demonstrated through several benchmark examples, including linear and non-linear fractional convection-diffusion, convection-diffusion-reaction, and nonlinear Fisher's equation. The numerical results confirm that the proposed method is stable, rapidly convergent, and highly accurate, outperforming several existing techniques in both efficiency and precision.https://jmm.guilan.ac.ir/article_9305_65082bf065e0cbe54d0cc6155545d721.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14220260501Modeling log-volatility with zero returns: empirical evidence for asymmetric SV and log-GARCH models787801940010.22124/jmm.2026.31979.2889ENAbdeljalilSettarLaboratory of mathematics, computer science and applications (LMCSA), FST Mohammedia,
Hassan II university, 20650 Casablanca, MoroccoSaraChegdalLaboratory of mathematics, computer science and applications (LMCSA), FST Mohammedia,
Hassan II university, 20650 Casablanca, MoroccoMustaphaKabilLaboratory of mathematics, computer science and applications (LMCSA), FST Mohammedia,
Hassan II university, 20650 Casablanca, MoroccoGhassaneBenrhmachDepartment of Mathematics and Statistics, College of Engineering, Abu Dhabi University, 59911 Abu
Dhabi, UAEJournal Article20251015In this work, we address the challenges posed by zero returns in both stochastic volatility (SV) and log-GARCH models in their asymmetric form. Building upon EM imputation for handling zero returns, we propose a unified approach that enhances parameter estimation robustness for both model classes. Specifically, we employ the Quasi-Maximum Likelihood (QML) estimation, incorporating the Kalman filter for both asymmetric SV and asymmetric log-GARCH models, to ensure robust parameter estimation even in the presence of zero returns. By comparing the performance of these models under our proposed framework, we provide new insights into their relative strengths in capturing the asymmetric volatility dynamics in the presence of zero returns. This contribution extends the existing literature by proposing a computational framework applicable to such models, based on a logarithmic specification of volatility.https://jmm.guilan.ac.ir/article_9400_bd9ba5bd36544b3dee3440a32fed3017.pdf