2020
8
4
0
0
1

Inner and outer estimations of the generalized solution sets and an application in economic
https://jmm.guilan.ac.ir/article_4058.html
10.22124/jmm.2020.16119.1409
1
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) 825828), 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.
0

345
361


Marzieh
DehghaniMadiseh
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran
University of Ahvaz, Ahvaz, Iran
Iran
m.dehghani@scu.ac.com
Interval arithmetic
Kaucher arithmetic
Cholesky decomposition
1

Partial correlation screening for varying coefficient models
https://jmm.guilan.ac.ir/article_4059.html
10.22124/jmm.2020.15692.1379
1
In this paper, we propose a twostage approach for feature selection in varying coefficient models with ultrahighdimensional predictors. Specifically, we first employ partial correlation coefficient for screening, and then penalized rank regression is applied for dimensionreduced 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.
0

363
376


Mohammad
Kazemi
Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Iran
m.kazemie64@yahoo.com
Big data
feature screening
partial correlation
rank regression
1

New approach to existence of solution for weighted Cauchytype problem
https://jmm.guilan.ac.ir/article_4063.html
10.22124/jmm.2020.14983.1393
1
In this paper, we consider a singular differential equation involving HilferKatugampola 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.
0

377
391


Sandeep P.
Bhairat
Faculty of Engineering Mathematics & Computer Science, Institute of Chemical Technology, Marathwada Campus, Jalna431 203 (M.S.) India
Iran
sp.bhairat@marj.ictmumbai.edu.in
Fractional integrals and derivatives
Picard iterative technique
singular fractional differential equation
Cauchytype problem
1

Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions
https://jmm.guilan.ac.ir/article_4157.html
10.22124/jmm.2020.16125.1407
1
This article is devoted to the study of a new class of nonlinear fractionalorder 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.
0

393
414


Hanan A.
Wahash
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India
Iran
hawahash86@gmail.com


Satish K.
Panchal
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India
Iran
drpanchalsk@gmail.com


Mohammed S.
Abdo
Department of Mathematics, Hodeidah University, AlHodeidah, Yemen
Iran
msabdo1977@gmail.com
Caputo fractional differential equation
integral boundary condition
existence of positive solution
control functions
Fixed point theorem
1

Solving Bratu's problem by double exponential Sinc method
https://jmm.guilan.ac.ir/article_4158.html
10.22124/jmm.2020.16221.1418
1
In this study, improved SincGalerkin and Sinccollocation methods are developed based on double exponential transformation to solve a onedimensional Bratutype 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 SincGalerkin is determined. Also the numerical approximations are compared with the best results reported in the literature. The results confirm that both the SincGalerkin and the Sinccollocation methods have the same accuracy, but they are significantly more accurate than the other existing methods.
0

415
433


Mohammad
Nabati
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
Iran
nabati@put.ac.ir


Soudabeh
Nikmanesh
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
Iran
soudabeh.nikmanesh@put.ac.ir
SincGalerkin
Sinccollocation
Bratu's problem
double exponential transformation
boundary value problems
1

Numerical solution of fractional partial differential equations by using radial basis functions combined with Legendre wavelets
https://jmm.guilan.ac.ir/article_4163.html
10.22124/jmm.2020.16806.1459
1
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 waveletsradial basis functions (WRBFs) directly. In the next step, the WRBFs 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.
0

435
454


Parisa
Rahimkhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
Iran
p.rahimkhani@alzahra.ac.ir


Yadollah
Ordokhani
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
Iran
ordokhani@alzahra.ac.ir
Fractional partial differential equations
radial basis functions
Legendre wavelets
numerical method
fractional integral operator
1

Regularity analysis and numerical resolution of the Pharmacokinetics (PK) equation for cisplatin with random coefficients and initial conditions
https://jmm.guilan.ac.ir/article_4173.html
10.22124/jmm.2020.16520.1433
1
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.
0

455
477


Saadeddine
Essarrout
Department of science computing, University Ibn Zohr, Agadir, Morocco
Iran
saadeddinemocasim@gmail.com


Said
Raghay
Department of Mathematics, University Cadi Ayyad, Marrakech, Morocco
Iran
s.raghay@uca.ac.ma


Zouhir
Mahani
Department of science computing, University Ibn Zohr, Agadir, Morocco
Iran
zouhir.mahani@gmail.com
Pharmacokinetics (PK) equation for cisplatin
stochastic collocation
Finite difference method
uncertainty quantification