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