University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 8 4 2020 09 01 Inner and outer estimations of the generalized solution sets and an application in economic 345 361 EN Marzieh Dehghani-Madiseh Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran m.dehghani@scu.ac.com 10.22124/jmm.2020.16119.1409 Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals and present algebraic completion of conventional interval arithmetic, allowing efficient solution for interval linear systems. In this paper, we use the Cholesky decomposition of a symmetric generalized interval matrix \${bf{A}}\$ introduced by Zhao et al. (A generalized Cholesky decomposition for interval matrix, Adv. Mat. Res. 479 (2012) 825--828), to construct the algebraic solution of the triangular interval linear system of equations. Also we utilize this decomposition to find inner and outer estimations of the generalized solution set of the symmetric interval linear systems. Finally some numerical experiments and an application in economic are given to show the efficiency of the presented technique. Interval arithmetic,Kaucher arithmetic,Cholesky decomposition https://jmm.guilan.ac.ir/article_4058.html https://jmm.guilan.ac.ir/article_4058_6f52e383583bbe79be4104c24973daa2.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 8 4 2020 09 01 Partial correlation screening for varying coefficient models 363 376 EN Mohammad Kazemi 0000-0002-9042-6552 Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran m.kazemie64@yahoo.com 10.22124/jmm.2020.15692.1379 In this paper, we propose a two-stage approach for feature selection in varying coefficient models with ultra-high-dimensional predictors. Specifically, we first employ partial correlation coefficient for screening, and then penalized rank regression is applied for dimension-reduced varying coefficient models to further select important predictors and estimate the coefficient functions. Simulation studies are carried out to examine the performance of proposed approach. We also illustrate it by a real data example. Big data,feature screening,partial correlation,rank regression https://jmm.guilan.ac.ir/article_4059.html https://jmm.guilan.ac.ir/article_4059_dd6e2e64992459a904f27771a310cd52.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 8 4 2020 09 01 New approach to existence of solution for weighted Cauchy-type problem 377 391 EN Sandeep P. Bhairat Faculty of Engineering Mathematics \& Computer Science, Institute of Chemical Technology, Marathwada Campus, Jalna--431 203 (M.S.) India sp.bhairat@marj.ictmumbai.edu.in 10.22124/jmm.2020.14983.1393 In this paper, we consider a singular differential equation involving Hilfer-Katugampola fractional derivative with the weighted initial condition. The Picard iterative technique has been successfully applied to obtain the existence of a unique solution. First, we derive an equivalent integral equation, then construct the successive approximations and use the ratio test to discuss its convergence. We demonstrate our results through a suitable illustrative example. Fractional integrals and derivatives,Picard iterative technique,singular fractional differential equation,Cauchy-type problem https://jmm.guilan.ac.ir/article_4063.html https://jmm.guilan.ac.ir/article_4063_06b6f9bdc9843bccefec98274fee504b.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 8 4 2020 09 01 Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions 393 414 EN Hanan A. Wahash 0000-0003-1927-7301 Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India hawahash86@gmail.com Satish K. Panchal Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India drpanchalsk@gmail.com Mohammed S. Abdo 0000-0001-9085-324X Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen msabdo1977@gmail.com 10.22124/jmm.2020.16125.1407 This article is devoted to the study of a new class of nonlinear fractional-order differential equations with integral boundary conditions involving a generalized version of the Caputo type fractional derivative with respect to another function \$h\$. In such a path, we transform the proposed problem into an equivalent integral equation. Then we build the upper and lower control functions of the nonlinear term without any monotone requirement except the continuity. By utilizing the method of upper and lower solutions, the fixed point theorems of Schauder and Banach, we obtain the existence and uniqueness of positive solutions for the problem at hand. Finally, we present some examples to illuminate our results. Caputo fractional differential equation,integral boundary condition,existence of positive solution,control functions,Fixed point theorem https://jmm.guilan.ac.ir/article_4157.html https://jmm.guilan.ac.ir/article_4157_bebd828095aa4e625a009cd6ec2f6d06.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 8 4 2020 09 01 Solving Bratu's problem by double exponential Sinc method 415 433 EN Mohammad Nabati Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran nabati@put.ac.ir Soudabeh Nikmanesh Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran soudabeh.nikmanesh@put.ac.ir 10.22124/jmm.2020.16221.1418 In this study, improved Sinc-Galerkin and Sinc-collocation methods are developed based on double exponential transformation to solve a one-dimensional Bratu-type equation. The properties of these methods are used to reduce the solution of the nonlinear problem to the solution of nonlinear algebraic equations. For simplicity in solving the nonlinear system, a matrix vector form of the nonlinear system is found. The upper bound of the error for the Sinc-Galerkin is determined. Also the numerical approximations are compared with the best results reported in the literature. The results confirm that both the Sinc-Galerkin and the Sinc-collocation methods have the same accuracy, but they are significantly more accurate than the other existing methods. Sinc-Galerkin,Sinc-collocation,Bratu's problem,double exponential transformation,boundary value problems https://jmm.guilan.ac.ir/article_4158.html https://jmm.guilan.ac.ir/article_4158_e8399a1e561c57b5b652f292b51cd848.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 8 4 2020 09 01 Numerical solution of fractional partial differential equations by using radial basis functions combined with Legendre wavelets 435 454 EN Parisa Rahimkhani Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran p.rahimkhani@alzahra.ac.ir Yadollah Ordokhani 0000-0002-5167-6874 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran ordokhani@alzahra.ac.ir 10.22124/jmm.2020.16806.1459 This paper presents an approximate method to solve a class of fractional partial differential equations (FPDEs). First, we introduce   radial basis functions (RBFs) combined with wavelets.  Next, we obtain fractional integral operator (FIO) of wavelets-radial basis functions (W-RBFs) directly.  In the next step, the W-RBFs and their FIO  are used to transform the problem under consideration into a  system of algebraic equations, which can be simply solved to achieve the solution of the problem.   Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the method. Fractional partial differential equations,radial basis functions,Legendre wavelets,numerical method,fractional integral operator https://jmm.guilan.ac.ir/article_4163.html https://jmm.guilan.ac.ir/article_4163_cf2d8fb51dcb3bbae07ade0a175d76a1.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 2382-9869 8 4 2020 09 01 Regularity analysis and numerical resolution of the Pharmacokinetics (PK) equation for cisplatin with random coefficients and initial conditions 455 477 EN Saadeddine Essarrout Department of science computing, University Ibn Zohr, Agadir, Morocco saadeddinemocasim@gmail.com Said Raghay Department of Mathematics, University Cadi Ayyad, Marrakech, Morocco s.raghay@uca.ac.ma Zouhir Mahani Department of science computing, University Ibn Zohr, Agadir, Morocco zouhir.mahani@gmail.com 10.22124/jmm.2020.16520.1433 In this paper, we study the pharmacokinetics equation for cisplatin (PKC) with random coefficients and initial conditions using the Stochastic Collocation method. We analyze the regularity of the solution with respect to the random variables.   The error estimate for the Stochastic Collocation method is proved using the regularity result and the error estimate for the Finite Difference method. Then, we provide the overall errors estimate and convergence is achieved as a direct result. Some numerical results are simulated to illustrate the theoretical analysis. We also propose a comparison between the stochastic and determinate solving process of PKC equation where we show the efficiency of our adopted method. Pharmacokinetics (PK) equation for cisplatin,stochastic collocation,Finite difference method,uncertainty quantification https://jmm.guilan.ac.ir/article_4173.html https://jmm.guilan.ac.ir/article_4173_5f82b702df359a9ee39fe6f1e3a426b1.pdf