ORIGINAL_ARTICLE
Inner and outer estimations of the generalized solution sets and an application in economic
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.
https://jmm.guilan.ac.ir/article_4058_6f52e383583bbe79be4104c24973daa2.pdf
2020-09-01
345
361
10.22124/jmm.2020.16119.1409
Interval arithmetic
Kaucher arithmetic
Cholesky decomposition
Marzieh
Dehghani-Madiseh
m.dehghani@scu.ac.com
1
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Partial correlation screening for varying coefficient models
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.
https://jmm.guilan.ac.ir/article_4059_dd6e2e64992459a904f27771a310cd52.pdf
2020-09-01
363
376
10.22124/jmm.2020.15692.1379
Big data
feature screening
partial correlation
rank regression
Mohammad
Kazemi
m.kazemie64@yahoo.com
1
Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
New approach to existence of solution for weighted Cauchy-type problem
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.
https://jmm.guilan.ac.ir/article_4063_06b6f9bdc9843bccefec98274fee504b.pdf
2020-09-01
377
391
10.22124/jmm.2020.14983.1393
Fractional integrals and derivatives
Picard iterative technique
singular fractional differential equation
Cauchy-type problem
Sandeep P.
Bhairat
sp.bhairat@marj.ictmumbai.edu.in
1
Faculty of Engineering Mathematics \& Computer Science, Institute of Chemical Technology, Marathwada Campus, Jalna--431 203 (M.S.) India
LEAD_AUTHOR
ORIGINAL_ARTICLE
Positive solutions for generalized Caputo fractional differential equations with integral boundary conditions
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.
https://jmm.guilan.ac.ir/article_4157_bebd828095aa4e625a009cd6ec2f6d06.pdf
2020-09-01
393
414
10.22124/jmm.2020.16125.1407
Caputo fractional differential equation
integral boundary condition
existence of positive solution
control functions
Fixed point theorem
Hanan A.
Wahash
hawahash86@gmail.com
1
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India
LEAD_AUTHOR
Satish K.
Panchal
drpanchalsk@gmail.com
2
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, (M.S), 431004, India
AUTHOR
Mohammed S.
Abdo
msabdo1977@gmail.com
3
Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen
AUTHOR
ORIGINAL_ARTICLE
Solving Bratu's problem by double exponential Sinc method
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.
https://jmm.guilan.ac.ir/article_4158_e8399a1e561c57b5b652f292b51cd848.pdf
2020-09-01
415
433
10.22124/jmm.2020.16221.1418
Sinc-Galerkin
Sinc-collocation
Bratu's problem
double exponential transformation
boundary value problems
Mohammad
Nabati
nabati@put.ac.ir
1
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
LEAD_AUTHOR
Soudabeh
Nikmanesh
soudabeh.nikmanesh@put.ac.ir
2
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
AUTHOR
ORIGINAL_ARTICLE
Numerical solution of fractional partial differential equations by using radial basis functions combined with Legendre wavelets
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.
https://jmm.guilan.ac.ir/article_4163_cf2d8fb51dcb3bbae07ade0a175d76a1.pdf
2020-09-01
435
454
10.22124/jmm.2020.16806.1459
Fractional partial differential equations
radial basis functions
Legendre wavelets
numerical method
fractional integral operator
Parisa
Rahimkhani
p.rahimkhani@alzahra.ac.ir
1
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
AUTHOR
Yadollah
Ordokhani
ordokhani@alzahra.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
LEAD_AUTHOR
ORIGINAL_ARTICLE
Regularity analysis and numerical resolution of the Pharmacokinetics (PK) equation for cisplatin with random coefficients and initial conditions
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.
https://jmm.guilan.ac.ir/article_4173_5f82b702df359a9ee39fe6f1e3a426b1.pdf
2020-09-01
455
477
10.22124/jmm.2020.16520.1433
Pharmacokinetics (PK) equation for cisplatin
stochastic collocation
Finite difference method
uncertainty quantification
Saadeddine
Essarrout
saadeddinemocasim@gmail.com
1
Department of science computing, University Ibn Zohr, Agadir, Morocco
LEAD_AUTHOR
Said
Raghay
s.raghay@uca.ac.ma
2
Department of Mathematics, University Cadi Ayyad, Marrakech, Morocco
AUTHOR
Zouhir
Mahani
zouhir.mahani@gmail.com
3
Department of science computing, University Ibn Zohr, Agadir, Morocco
AUTHOR