University of GuilanJournal of Mathematical Modeling2345-394X12320240901Targeted drug delivery in multi-layer capsules: an analytical and numerical study387403765710.22124/jmm.2024.25716.2284ENEbrahimAzhdariDepartment of Mathematics, Salman Farsi University of Kazerun, Fars, Kazerun, IranAramEmamiDepartment of Mathematics, Salman Farsi University of Kazerun, Fars, Kazerun, IranJournal Article20231003Recently, polymeric multi-layer capsules have gained a great deal of attention from the life science community. Furthermore, myriad interesting systems have appeared in the literature with biodegradable components and biospecific functionalities. In the present work, we presented a mathematical model of drug release from a multi-layer capsule into a target tissue. The diffusion problem was described by a system of coupled partial differential equations, Fickian and non-Fickian, which we solved numerically via nonuniform finite differences method. Energy estimates were further established for the coupled system and also, the convergence properties of the proposed numerical method were justified. We ultimately demonstrated the qualitative behavior of the system.https://jmm.guilan.ac.ir/article_7657_b1fe93304162585b07b4606164278945.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901An efficient numerical method based on cubic B--splines for the time--fractional Black--Scholes European option pricing model405417767710.22124/jmm.2024.26551.2341ENHamedPayandehdoost MasoulehDepartment of Accounting, Bandaranzali Branch, Islamic Azad University, Bandaranzali, Iran0000-0002-9578-0702MojganEsmailzadehDepartment of Applied Mathematics, Bandaranzali Branch, Islamic Azad
University, Bandaranzali, Iran0000-0003-0183-5985Journal Article20240122In this study, we develop a precise and effective numerical approach to solve the time--fractional Black--Scholes equation, which is used to calculate European options. The method employs cubic B-spline collocation for spatial discretization and a finite difference method for time discretization. An analysis of the method's stability is conducted. Finally, two numerical examples are included to show the effectiveness and applicability of the suggested method.https://jmm.guilan.ac.ir/article_7677_54cb32864ccf7e134e2b8acef3dd8c9e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Dynamics and bifurcations of a discrete-time neural network model with a single delay419430767810.22124/jmm.2024.26038.2309ENJavadHadadiDepartment of Mathematical Sciences, Shahrekord University, Shahrekord, Iran0009-0007-4862-4815RezaKhoshsiar GhazianiDepartment of Mathematical Sciences, Shahrekord University, Shahrekord, IranJavadAlidoustiDepartment of Mathematical Sciences, Shahrekord University, Shahrekord, IranZohrehEskandariDepartment of Mathematics, Faculty of Science, Fasa University, Fasa, Iran0000-0003-0373-8038Journal Article20231120In the present study, we analyze dynamics and bifurcations of a discrete-time Hopfield neural network based on two neurons and the same time delay. We determine stability and bifurcations of the system consisting flip, pitchfork and Neimark-Sacker bifurcations. The normal form coefficients for the all bifurcations are calculated using reducing to the corresponding center manifold, then these coefficients are numerically obtained using MatContM. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.https://jmm.guilan.ac.ir/article_7678_6b6e4de1d5d9b83938cf64f9da30dc26.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Application of compact local integrated RBFs technique to solve fourth-order time-fractional diffusion-wave system431449767910.22124/jmm.2024.25417.2260ENMostafaAbbaszadehDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), No. 424, Hafez Ave., 15914 Tehran, IranAliRezaBagheri SalecDepartment of Mathematics, Faculty of Basic Scince, University of Qom, Alghadir Blvd., Qom, IranAlaa SalimJeburDepartment of Mathematics, Faculty of Basic Scince, University of Qom, Alghadir Blvd., Qom, IranJournal Article20230829The main aim of the current paper is to apply the compact local integrated RBFs technique to the numerical solution of the fourth-order time-fractional diffusion-wave system. A finite difference formula is employed to obtain a time-discrete scheme. The stability and convergence rate of the semi-discrete plan are proved by the energy method. A new unknown variable is defined to obtain a second-order system of PDEs. Then, the compact local integrated radial basis functions (RBFs) is used to approximate the spatial derivative. The utilized numerical method is a truly meshless technique. The numerical approach put forth is genuinely meshless, allowing for the utilization of irregular physical domains in obtaining numerical solutions.https://jmm.guilan.ac.ir/article_7679_d56fabce86a51dcbbaca1c97aece1f11.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901On differential-integral optimal control problems451462770510.22124/jmm.2024.26520.2338ENMohammedShehataDepartment of Basic Science, Bilbeis Higher Institute For Engineering, Sharqia, EgyptJournal Article20240120In this paper, we will study the optimal control problem of a system containing a differential integral (D-I) operator. We will deduce the necessary optimality conditions and apply it first to the problem of minimum energy to find the lowest energy for an electrical circuit containing a resistor, a coil and a capacitor (RLC circuit), and second to the problem of the minimum time to transfer electrical current in RLC circuit from one state to another in the shortest possible time. https://jmm.guilan.ac.ir/article_7705_ff7dc9fc66e0d1e655efce51f03a2821.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Introducing three new smoothing functions: Analysis on smoothing-Newton algorithms463479770610.22124/jmm.2024.26827.2361ENNurullahYilmazDepartment of Mathematics, Suleyman Demirel University, Isparta, Turkey0000-0001-6429-7518Journal Article20240222In this paper, we focus on solving the system of absolute value equations (AVE), which is one of the most popular classes of nonlinear equations. First, a new smoothing technique with three different smoothing functions is introduced, and the AVE is transformed into a family of parametrized smooth equations with the help of these smoothing functions. Then, a smoothing Newton-type algorithm with hybridized inexact line search is developed based on the proposed smoothing technique. The numerical experiments have been carried out on some well-known and randomly generated test problems, and the results are analyzed in terms of line search techniques. The numerical results show that the proposed hybrid approach is more efficient than the other algorithms.https://jmm.guilan.ac.ir/article_7706_5065fb3b8cf1a821fbb8fb8e38c86dff.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Tensor splitting preconditioners for multilinear systems481499773710.22124/jmm.2024.23603.2104ENSaeedKarimiMathematics Department, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, IranEisaKhosravi DehdeziMathematics Department, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran0000-0002-1106-4451Journal Article20230110In this paper, we propose some new preconditioners for solving multilinear system $\mathcal{A}\mathbf{x}^{m-1}=\mathbf{b}$. These preconditioners are based on tensor splitting. We also present some theorems for analyzing and convergence of the preconditioned Jacobi-, Gauss-Seidel-, and SOR-type iterative methods. Numerical examples are presented to verify the efficiency of the proposed preconditioned methods.https://jmm.guilan.ac.ir/article_7737_d9d1020ae30bfa2126c9a0aaafdb6bcc.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901A uniformly convergent numerical scheme for singularly perturbed parabolic turning point problem501516778910.22124/jmm.2024.26669.2349ENSisay KetemaTesfayeDepartment of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia0009-0005-0602-3013Gemechis FileDuressaDepartment of Mathematics, Jimma University, Jimma, Ethiopia0000-0003-1889-4690Mesfin MekuriaWoldaregayDepartment of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia0000-0002-6555-7534Tekle GemechuDinkaDepartment of Applied Mathematics, Adama Science and Technology University, Adama, EthiopiaJournal Article20240208A uniformly convergent numerical scheme is developed for solving a singularly perturbed parabolic turning point problem. The properties of continuous solutions and the bounds of the derivatives are discussed. Due to the presence of a small parameter as a multiple of the diffusion coefficient, it causes computational difficulty when applying classical numerical methods. As a result, the scheme is formulated using the Crank-Nicolson method in the temporal discretization and an exponentially fitted finite difference method in the space on a uniform mesh. The existence of a unique discrete solution is guaranteed by the comparison principle. The stability and convergence analysis of the method are investigated. Two numerical examples are considered to validate the applicability of the scheme. The numerical results are displayed in tables and graphs to support the theoretical findings. The scheme converges uniformly with order one in space and two in time.https://jmm.guilan.ac.ir/article_7789_08c822753ae15319c4e38ba08a3e20f6.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Lions's partial derivatives with respect to probability measures for general mean-field stochastic control problem517532780410.22124/jmm.2024.27136.2390ENFatihaKorichiLaboratory of Mathematical Analysis, Probability and Optimizations, Department of Mathematics, University of Biskra, PO Box 145, Biskra 7000, AlgeriaMokhtarHafayedLaboratory of Mathematical Analysis, Probability and Optimizations, Department of Mathematics, University of Biskra, PO Box 145, Biskra 7000, Algeria0000-0002-8915-9530Journal Article20240402In this paper, a necessary stochastic maximum principle for stochastic model governed by mean-field nonlinear controlled It$\rm{\ddot{o}}$-stochastic differential equations is proved. The coefficients of our model are nonlinear and depend explicitly on the control variable, the state process as well as of its probability distribution. The control region is assumed to be bounded and convex. Our main result is derived by applying the Lions's partial-derivatives with respect to random measures in Wasserstein space. The associated It$\rm{\ddot{o}}$-formula and convex-variation approach are applied to establish the optimal control.https://jmm.guilan.ac.ir/article_7804_f1e54aa063e314582a94b019f31c9ccd.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Unconditionally stable finite element method for the variable-order fractional Schrödinger equation with Mittag-Leffler kernel533550780510.22124/jmm.2024.27385.2413ENGholamrezaKaramaliFaculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology, South Mehrabad, Tehran, Iran0009-0000-2637-8755HadiMohammadi-FirouzjaeiFaculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology,
South Mehrabad, Tehran, Iran0000-0002-7018-500XJournal Article20240504The Schrödinger equation with variable-order fractional operator is a challenging problem to be solved numerically. In this study, an implicit fully discrete continuous Galerkin finite element method is developed to tackle this equation while the fractional operator is expressed with a nonsingular Mittag-Leffler kernel. To begin with, the finite difference scheme known as the L1 formula is employed to discretize the temporal term. Next, the continuous Galerkin method is used for spatial discretization. This combination ensures accuracy and stability of the numerical approximation. Our next step is to conduct a stability and error analysis of the proposed scheme. Finally, some numerical results are carried out to validate the theoretical analysis.https://jmm.guilan.ac.ir/article_7805_f341d6355625fc2f86a4c135c7efd1ae.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Stochastic permanence and extinction of a hybrid predator-prey system with jumps551564783210.22124/jmm.2024.27509.2421ENShengWangSchool of Mathematics and Information Science, Henan Polytechnic University (HPU), Jiaozuo, 454003, P.R. ChinaBaoliLeiSchool of Mathematics and Information Science, Henan Polytechnic University (HPU), Jiaozuo, 454003, P.R. ChinaJournal Article20240520This paper concerns the dynamics of a stochastic Holling-type II predator-prey system with Markovian switching and L{e}vy noise. First, the existence and uniqueness of global positive solution to the system with the given initial value is proved.<br />Then, sufficient conditions for extinction and stochastic permanence of the system are obtained. Finally, an example and its numerical simulations are given to support the theoretical results.https://jmm.guilan.ac.ir/article_7832_ac4e3a1b923ff00cb6a1352d393192fa.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X12320240901Evaluating cost efficiency of decision-making units in an uncertain environment565582786710.22124/jmm.2024.26529.2340ENJafarPourmahmoudDepartment of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran0000-0003-4241-1871SeyedhadiAramiDepartment of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranJournal Article20240121The efficiency evaluation of organizational units provides managers with a perspective on the current state of the organization and solutions for their improvement. One of the methods of organizational evaluation is to determine the organization's minimum cost or cost efficiency. Cost efficiency in practice can be calculated when the input prices are available. In traditional models of cost efficiency, input and output data are crisp. However, there are situations where input and/or output may be imprecise. For such cases, experts are invited to model their opinion. Then uncertainty theory can be applied which is introduced by Liu as a mathematical branch rationally dealing with belief degrees. In this paper, a model is proposed to estimate the cost of decision-making units in the uncertain environment, where inputs and outputs are uncertain but the input prices are crisp. Several theorems are presented to discuss some features of the introduced model. When the data has a linear distribution, the cost efficiencies of the decision-making units are calculated. Also, the model is implemented on two numerical examples. The obtained results are compared with previous results. Finally, in the presence of input prices, a different cost efficiency score for the decision-making units is obtained. The proposed model helps decision-makers to improve their performance by using experts' opinions.https://jmm.guilan.ac.ir/article_7867_664530ea2a780deac5489509e4ed16f0.pdf