J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.16119.1409 Research Paper Inner and outer estimations of the generalized solution sets and an application in economic Inner and outer estimations of the generalized solution sets Dehghani-Madiseh Marzieh Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran 01 09 2020 8 4 345 361 31 03 2020 16 05 2020 Copyright © 2020, دانشگاه گیلان. 2020 https://jmm.guilan.ac.ir/article_4058.html

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
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.15692.1379 Research Paper Partial correlation screening for varying coefficient models Partial correlation screening for varying coefficient models Kazemi Mohammad Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran 01 09 2020 8 4 363 376 11 02 2020 23 05 2020 Copyright © 2020, دانشگاه گیلان. 2020 https://jmm.guilan.ac.ir/article_4059.html

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
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.14983.1393 Research Paper New approach to existence of solution for weighted Cauchy-type problem New approach to existence of solution for weighted Cauchy-type problem Bhairat Sandeep P. Faculty of Engineering Mathematics \& Computer Science, Institute of Chemical Technology, Marathwada Campus, Jalna--431 203 (M.S.) India 01 09 2020 8 4 377 391 06 03 2020 19 05 2020 Copyright © 2020, دانشگاه گیلان. 2020 https://jmm.guilan.ac.ir/article_4063.html

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
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.16125.1407 Research Paper Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions Positive solutions of generalized Caputo FDEs Wahash Hanan A. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India Panchal Satish K. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India Abdo Mohammed S. Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen 01 09 2020 8 4 393 414 26 04 2020 22 06 2020 Copyright © 2020, دانشگاه گیلان. 2020 https://jmm.guilan.ac.ir/article_4157.html

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
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.16221.1418 Research Paper Solving Bratu's problem by double exponential Sinc method Solving Bratu's problem through DE Sinc method Nabati Mohammad Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran Nikmanesh Soudabeh Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran 01 09 2020 8 4 415 433 10 04 2020 10 07 2020 Copyright © 2020, دانشگاه گیلان. 2020 https://jmm.guilan.ac.ir/article_4158.html

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
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.16806.1459 Research Paper Numerical solution of fractional partial differential equations by using radial basis functions combined with Legendre wavelets Numerical solution of fractional PDEs Rahimkhani Parisa Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Ordokhani Yadollah Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran 01 09 2020 8 4 435 454 12 06 2020 29 06 2020 Copyright © 2020, دانشگاه گیلان. 2020 https://jmm.guilan.ac.ir/article_4163.html

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
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2020.16520.1433 Research Paper Regularity analysis and numerical resolution of the Pharmacokinetics (PK) equation for cisplatin with random coefficients and initial conditions Regularity analysis and numerical resolution of the PK equation Essarrout Saadeddine Department of science computing, University Ibn Zohr, Agadir, Morocco Raghay Said Department of Mathematics, University Cadi Ayyad, Marrakech, Morocco Mahani Zouhir Department of science computing, University Ibn Zohr, Agadir, Morocco 01 09 2020 8 4 455 477 12 05 2020 10 07 2020 Copyright © 2020, دانشگاه گیلان. 2020 https://jmm.guilan.ac.ir/article_4173.html

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