University of GuilanJournal of Mathematical Modeling2345-394X9120210101A moving kriging interpolation-based meshfree method for solving two-phase elasticity system112418610.22124/jmm.2020.17088.1484ENAmenehTaleeiDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranJournal Article20200714The elasticity interface problems occur frequently when two or more materials meet. In this paper, a meshfree point collocation method based on moving kriging interpolation is proposed for solving the two-phase elasticity system with an arbitrary interface. The moving kriging shape function and its derivatives are constructed by moving kriging interpolation technique. Since the shape function possesses the Kronecker delta property then the Dirichlet boundary condition can be implemented directly and easily. Numerical results demonstrate the accuracy and efficiency of the proposed method for the studied problems with constant and variable coefficients.https://jmm.guilan.ac.ir/article_4186_40f9b084970d75853cfa5b94d6b8ee6a.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101A combined dictionary learning and TV model for image restoration with convergence analysis1330418710.22124/jmm.2020.15408.1369ENSouadMohaouiDepartment of mathematics, University of Cadi Ayad, Marrakesh, MoroccoAbdelilahHakimDepartment of mathematics, University of Cadi Ayad, Marrakesh, MoroccoSaidRaghayDepartment of mathematics, University of Cadi Ayad, Marrakesh, MoroccoJournal Article20200109We consider in this paper the $l_0$-norm based dictionary learning approach combined with total variation regularization for the image restoration problem. It is formulated as a nonconvex nonsmooth optimization problem. Despite that this image restoration model has been proposed in many works, it remains important to ensure that the considered minimization method satisfies the global convergence property, which is the main objective of this work. Therefore, we employ the proximal alternating linearized minimization method whereby we demonstrate the global convergence of the generated sequence to a critical point. The results of several experiments demonstrate the performance of the proposed algorithm for image restoration.https://jmm.guilan.ac.ir/article_4187_8d48376485cc61654259b0f2dd2b02e0.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101Lower bound approximation of nonlinear basket option with jump-diffusion3144422610.22124/jmm.2020.16126.1408ENYasserTaherinasabDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, IranAli RezaSoheiliDepartment of applied mathematics
Ferdowsi university of Mashhad
Mashhad and The Center of Excellence on Modeling and Control Systems, Ferdowsi University of Mashhad, IranMohammadAminiDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20200330We extend the method presented by Xu and Zheng (Int. J. Theor. Appl. Finance 17 (2014) 21--36) for the general case. We develop a numerical-analytic formula for pricing nonlinear basket options with jump-diffusion model. We derive an easily computed method by using the asymptotic expansion to find the approximate value of the lower bound of nonlinear European basket call prices since a nonlinear basket option is generally not closed-form. We use Split Step Backward Euler and Compensated Split Step Backward Euler methods with Monte Carlo simulation to check the validity of the presented method.<br /><br />https://jmm.guilan.ac.ir/article_4226_1b4d910cad60b8833e6f28bc1332a38b.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101Almost periodic positive solutions for a time-delayed SIR epidemic model with saturated treatment on time scales4560423010.22124/jmm.2020.16271.1420ENKapula RajendraPrasadCollege of Science and Technology, Department of Applied Mathematics, Andhra University, Visakhapatnam, India-530003MahammadKhuddushCollege of Science and Technology, Department of Applied Mathematics, Andhra University, Visakhapatnam, India-530003Kuparala VenkataVidyasagarCollege of Science and Technology, Department of Applied Mathematics, Andhra University, Visakhapatnam, India-530003 and Department of Mathematics, Government Degree College for Women, Marripalem, Koyyuru Mandal, Visakhapatnam, India-531116Journal Article20200415In this paper, we study a non-autonomous time-delayed SIR epidemic model which involves almost periodic incidence rate and saturated treatment function on time scales. By utilizing some dynamic inequalities on time scales, sufficient conditions are derived for the permanence of the SIR epidemic model and we also obtain the existence and uniform asymptotic stability of almost periodic positive solutions for the addressed SIR model by Lyapunov functional method. Finally numerical simulations are given to demonstrate our theoretical results.https://jmm.guilan.ac.ir/article_4230_9b40bcb9a3cfdf4fe20b7bb07b5f0e64.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101Solving the Basset equation via Chebyshev collocation and LDG methods6179423110.22124/jmm.2020.17135.1489ENMohammadIzadiDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranMehdiAfsharDepartment of Mathematics and Statistics, Zanjan Branch , Islamic Azad University, Zanjan, Iran.Journal Article20200718Two different numerical methods are developed to find approximate solutions of a class of linear fractional differential equations (LFDEs) appearing in the study of the generalized Basset force, when a sphere sinks in a viscous fluid. In the first one, using the Chebyshev bases, the collocation points, and the matrix operations, the given LFDE reduces to a matrix equation while in the second one, we employ the local discontinuous Galerkin (LDG) method, which uses the natural upwind flux yielding a stable discretization. Unlike the first method, in the latter method we are able to solve the problem element by element locally and there is no need to solve a full global matrix. The efficiency of the proposed algorithms are shown via some numerical examples.https://jmm.guilan.ac.ir/article_4231_c43909580b688d457545bf3290f7da3e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101An RBF approach for oil futures pricing under the jump-diffusion model8192423410.22124/jmm.2020.15948.1396ENMohammadKarimnejad EsfahaniDepartment of Mathematics, Allameh Tabataba'i University, IranAbdolsadehNeisyDepartment of Mathematics, Allameh Tabataba'i University, IranStefanoDe MarchiDepartment of Mathematics "Tullio Levi-Civita", University of Padova, ItalyJournal Article20200307In this paper, our concern is to present and solve the problem of pricing oil futures. For this purpose, firstly we suggest a model based on the well-known Schwartz's model, in which the oil futures price is based on spot price of oil and convenience yield, however, the main difference here is that we have assumed that the former was imposed to some jumps, thus we added a jump term to the model of spot price. In our case, the oil future price model would be a Partial Integral Differential Equation (PIDE). Since, no closed form solution can be suggested for these kind of equations, we desire to solve our model with an appropriate numerical method. Although Finite Differences (FD) or Finite Elements (FE) is a common method for doing so, in this paper, we propose an alternative method based on Radial Basis Functions (RBF).https://jmm.guilan.ac.ir/article_4234_4601c4bfd9ea42954940b31531be8371.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101Caputo-Hadamard fractional differential equation with impulsive boundary conditions93106423610.22124/jmm.2020.16449.1447ENAnkit KumarNainDepartment of Mathematics and Scienti fic Computing,
National Institute of Technology, Hamirpur, HP-177005, IndiaRamesh KumarVatsDepartment of Mathematics and Scienti fic Computing,
National Institute of Technology, Hamirpur, HP-177005, IndiaAvadheshKumarDepartment of Mathematics and Computer Science,
Sri Sathya Sai Institute of Higher Learning, Prasanthi Nilayam(A.P.) - 515134, IndiaJournal Article20200603This manuscript is concerned about the study of the existence and uniqueness of solutions for fractional differential equation involving Caputo Hadamard fractional operator of order $1 < \vartheta \leq 2$ with impulsive boundary conditions. The existence results are established firstly through the Banach Contraction Principle and then using Schauder's fixed point theorem. We present some examples to demonstrate the application of our main results.https://jmm.guilan.ac.ir/article_4236_d2a8b8fe278217652dd5a92bca133354.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101Stability for coupled systems on networks with Caputo-Hadamard fractional derivative107118423910.22124/jmm.2020.17303.1500ENHadjerBelbaliLaboratoire de Mathematiques et Sciences appliquees, University of Ghardaia, AlgeriaaMaamarBenbachirFaculty of Sciences, Saad Dahlab University, Blida, AlgeriaJournal Article20200803This paper discusses stability and uniform asymptotic stability of the trivial solution of the following coupled systems of fractional differential equations on networks<br />\begin{equation*}<br /> \left\{<br /> \begin{array}{l l l}<br /> ^{cH}D^{\alpha} x_{i}=f_{i}(t,x_{i})+\sum\limits_{j=1}^{n}g_{ij}(t,x_{i},x_{j}),&t> t_{0}, \\ <br /> x_{i}(t_{0})=x_{i0},<br /> \end{array}<br /> \right.<br /> \end{equation*}<br /> where $^{cH}D^{\alpha} $ denotes the Caputo-Hadamard fractional derivative of order $ \alpha $, $ 1<\alpha\leq 2 $, $ i=1,2,\dots,n$, and $ f_{i}:\mathbb{R}_{+}\times\mathbb{R}^{m_i} \to \mathbb{R}^{m_i} $, $ g_{ij} : \mathbb{R}_{+}\times \mathbb{R}^{m_i}\times \mathbb{R}^{m_j} \to \mathbb{R}^{m_i} $ are given functions. Based on graph theory and the classical Lyapunov technique, we prove stability and uniform asymptotic stability under suitable sufficient conditions. We also provide an example to illustrate the obtained results.https://jmm.guilan.ac.ir/article_4239_873afc1dd63e1fdb9b46a41d5d4f8369.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101On global existence and Ulam-Hyers stability of $\Psi-$Hilfer fractional integrodifferential equations119135425610.22124/jmm.2020.16092.1405ENVinodVijaykumar KharatDepartment~of~Mathematics, N. B. Navale Sinhgad College of Engg., Kegaon, Solapur-413255, India (M.S.)AnandRajshekhar ReshimkarDepartment of Mathematics, D. B. F. Dayanand College of Arts and Science, Solapur-413002, India (M.S.)Journal Article20200329In this sense, for this new fractional integrodifferential equation, we study the Ulam-Hyers and Ulam-Hyers-Rassias stability via successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and uniqueness via $\epsilon-$approximated solution.https://jmm.guilan.ac.ir/article_4256_0e004567c0b16e881392e5d615eb5536.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X9120210101Mathematical models for the variable weights version of the inverse minimax circle location problem137144425710.22124/jmm.2020.16786.1455ENMehranehGholamiFaculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, IranJafarFathaliFaculty of Mathematical Sciences, Shahrood University of Technology, University Blvd., Shahrood, IranJournal Article20200610This paper deals with the case of variable weights of the inverse model of the minimax circle location problem. The goal of the classic minimax circle location problem is finding a circle in the plane such that the maximum weighted distance from a given set of existing points to the circumference of the circle is minimized. In the corresponding inverse model, a circle is given and we should modify the weights of existing points with minimum cost, such that the given circle becomes optimal. The radius of the given circle can be fixed or variable. In this paper, both of these cases are investigated and mathematical models are presented for solving them.https://jmm.guilan.ac.ir/article_4257_beb557a38d1688d48e78ed4238d7ba18.pdf