https://jmm.guilan.ac.ir/ Journal of Mathematical Modeling en daily 1 Fri, 01 May 2026 00:00:00 +0330 Fri, 01 May 2026 00:00:00 +0330 https://jmm.guilan.ac.ir/article_9002.html An 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_9196.html In 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_9198.html This 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 $\mathfrak{R_0}$ 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_9201.html This study examines a class of predator models that incorporate cooperative predation withinspecialized 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_9215.html Nonlinear 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_9222.html This 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_9233.html This 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_9240.html A 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_9243.html This 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 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 effectiveness https://jmm.guilan.ac.ir/article_9245.html Transaction 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_9247.html This 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_9264.html In this paper, we consider the generalized Celis-Dennis-Tapia problemwhich is the problem of minimizing a nonconvex quadratic function subject totwo quadratic inequality constraints, one of which being convex. When there isa positive duality gap, by exploiting an equivalent form of the dual Lagrangianproblem, we propose to improve the dual bound by adding one or two linear cutsto the Lagrangian relaxation. The present work is motivated by and generalizesthe results of [14] for the problem with two strictly convex quadratic constraints.Our main contribution is to show that one can include the feasible region in a con-vex set and then follow the approach in [14] to construct the linear cuts based onsupporting hyperplanes of the convex set. Numerical experiments are conductedto assess the quality of the proposed bounds. https://jmm.guilan.ac.ir/article_9269.html This study addresses the integrated hub location and drone delivery problem, an area with few5prior 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_9289.html This 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.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_9295.html This study contributes to epidemic control literature by introducing a time-varying inci-dence rate and establishing global controllability of the nonlinear SIR system, offering apractical framework for adaptive control strategies. We derive explicit solutions for partialcontrollability, demonstrating the feasibility of controlling the infected population, pro-viding guidance for outbreak management. Numerical methods exploiting an algorithmicapproach achieve full control, targeting a desired state (Sd, Id). A novel hybrid methodintegrates analytical solutions with algorithmic optimization, leveraging explicit expres-sions for I(t) and S(t) to enhance precision and efficiency of epidemic control strategies,advancing adaptive management approaches https://jmm.guilan.ac.ir/article_9299.html This 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_9301.html The 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_9302.html We 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_9305.html This 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_9400.html In 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_9403.html This study is focused on the bending response of electro-magneto-elastic nanobeams exposedto 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_9404.html Fractional 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_9405.html Optimal 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_9407.html The 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_9421.html This paper investigates a novel distributed-order time-fractional cable equation involving both Caputo and Riemann–Liouville fractional derivatives, which models complex diffusion and memory effects in various physical andbiological 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 schemeis 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 schemethat effectively combines the advantages of convolution quadrature with classical finite difference methods. A detailedconvergence and stability analysis of the numerical method is presented using an energy-based approach and a discretefractional Gr¨onwall inequality. The method is proven to be unconditionally stable and achieves optimal convergencerates in both time and space. Numerical simulations confirm the theoretical predictions and demonstrate the accuracyand efficiency of the scheme in capturing the underlying fractional dynamics. The proposed framework offers a powerfuland flexible tool for the numerical simulation of fractional-order systems with distributed memory, and can be extendedto a wide range of multi-term and distributed-order fractional partial differential equations. https://jmm.guilan.ac.ir/article_9426.html In 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_9429.html The present investigation examines the Michaelis-Menten kinetics response diffusion problemin a planar, spherical framework by employing mathematical model. The substrate concentrationis found to have straightforward outcomes with the Michaelis constant, modified Sherwoodnumber, and Thiele modulus. Here, the analytical approximation for the non-dimensional substrateconcentration and unitless effectiveness factor are determined via the new approximateanalytical methodology for steady-state (Ananthaswamy - Sivasankari method ASM) and Homotopywith Laplace transform method for non-steady state. Additionally, juxtaposition betweenthe analytical approximation and numerical simulation is provided. There is a good correlationbetween the numerical results and the approximate analytical result. https://jmm.guilan.ac.ir/article_9452.html In 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_9454.html Clustering 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_9477.html In 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_9497.html This study addresses the critical trade-off between financial returns and operational stability in capital-intensive project portfolios. We propose a novel convex Mixed-Integer QuadraticallyConstrained Programming (MIQCP) framework that unifies Net Present Value (NPV) maximization, strict self-financing, and direct resource variance minimization. Unlike existing non-convex orheuristic models, our approach endogenizes flexible phasing strategies and introduces a dual-buffermechanism to protect both liquidity and resource capacity. By exploiting the positive semi-definiteproperties of the quadratic constraints, we ensure global optimality for portfolios with 50+ activities. Computational results reveal a significant ”constrainedness” effect, where tighter financial andprecedence 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_9498.html In 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_9543.html ‎The problem of finding the space‎- ‎or time-dependent control parameter in partial differential equations has increasingly appeared in physical‎‎phenomena‎, ‎for example‎, ‎in the study of control theory‎, ‎heat conduction process‎, ‎and‎‎chemical diffusion‎. ‎This study aims to construct an efficient numerical method to determine a time-dependent source term in a time fractional diffusion‎‎equation 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_9544.html Mathematical 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_9545.html In 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_9556.html Krylov 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_9563.html In 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_9570.html In 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_9585.html This 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_9592.html To 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.