2019
7
1
0
0
1

Existence and continuation of solutions of Hilfer fractional differential equations
https://jmm.guilan.ac.ir/article_3048.html
10.22124/jmm.2018.9220.1136
1
In the present paper we consider initial value problems for Hilfer fractional differential equations and for system of Hilfer fractional differential equations. By using equivalent integral equations and some fixed point theorems, we study the local existence of solutions. We extend these local existence results globally with the help of continuation theorems and generalized Gronwall inequality.
0

1
20


Sandeep P.
Bhairat
Department of mathematics, Institute of Chemical Technology, Mumbai400 019 (M.S.), India
Iran
sp.bhairat@ictmumbai.edu.in
Fractional differential equations
local existence
continuation theorem
global solutions
1

Bases for polynomialbased spaces
https://jmm.guilan.ac.ir/article_3049.html
10.22124/jmm.2018.11242.1189
1
Since it is wellknown that the Vandermonde matrix is illconditioned, this paper surveys the choices of other bases. These bases are datadependent and are categorized into discretely $ell^2$orthonormal and continuously $L^2$orthonormal bases. The first one is defined via a decomposition of the Vandermonde matrix while the latter is given by a decomposition of the Gramian matrix corresponding to monomial bases. A discussion of various matrix decomposition (e.g. Cholesky, QR and SVD) provides a variety of different bases with different properties. Special attention is given to duality. Numerical results show that the matrices of values of the new bases have smaller condition numbers than the common monomial bases. It can also be pointed out that the new introduced bases are good candidates for interpolation.
0

21
34


Maryam
Mohammadi
Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
Iran
m.mohammadi@khu.ac.ir


Maryam
Bahrkazemi
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
Iran
m.bahrkazemi@alumni.iust.ac.ir
Polynomial interpolation
interpolation bases
monomial bases
duality
Vandermonde matrix
Gramian Matrix
matrix decomposition
1

A new twoparameter distribution: properties and applications
https://jmm.guilan.ac.ir/article_3102.html
10.22124/jmm.2018.9994.1148
1
In this paper, a new twoparameter lifetime distribution called ``the exponentiated Shanker distribution" is suggested. The new distribution has an increasing, decreasing and bathtubshaped hazard rate function (hrf) for modeling lifetime data. Various mathematical and statistical properties of the proposed distribution including its hrf, complete and incomplete moments, skewness and kurtosis, mean deviations, Bonferroni and Lorenz curves are discussed. Estimation of its parameters is also discussed using the method of maximum likelihood estimation and a simulation study is given. Finally, two applications of the new distribution are presented using two real data sets. The results also confirmed the suitability of the proposed model for the real data sets.
0

35
48


Anita
Abdollahi Nanvapisheh
Department of Statistics, Islamic Azad University, Tehran north branch, Tehran, Iran
Iran
anita.abdollahi@yahoo.com


S.M.T.K.
MirMostafaee
Department of Statistics, University of Mazandaran, P.O. Box 474161467, Babolsar, Iran
Iran
m.mirmostafaee@umz.ac.ir


Emrah
Altun
Department of Statistics, Bartin University, Bartin 74100, Turkey
Iran
emrahaltun@bartin.edu.tr
Exponentiated Shanker distribution
goodness of fit
lifetime data
mathematical and statistical characteristics
parameter estimation
1

Global dynamics of a mathematical model on smoking: impact of antismoking campaign
https://jmm.guilan.ac.ir/article_3187.html
10.22124/jmm.2018.10117.1153
1
We propose and analyze a mathematical model to study the dynamics of smoking behavior under the influence of educational and media programs. Proposed mathematical model subdivides the total population into potential smokers, smokers and those smokers who quit smoking permanently. The biologically feasible equilibrium points are computed and their stability is analyzed and discussed. The theoretical analysis of the model reveals that the smokingfree equilibrium is stable when a threshold, termed as the smokersgeneration number, is less than unity, and unstable if this threshold value is greater than unity. Moreover, number of smokers may be effectively controlled by keeping the smokers generation number less than unity. Analytical findings are justified by numerical simulation.
0

49
62


Vinay
Verma
Department of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki225003, India
Iran
vinay.verma09@rediffmail.com


Archana
Bhadauria
Department of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki225003, India
Iran
archanasingh93@yahoo.co.in
Smoking
Education
media
global Stability
Lyapunov function
1

Valid implementation of the Sinccollocation method to solve linear integral equations by the CADNA library
https://jmm.guilan.ac.ir/article_3191.html
10.22124/jmm.2018.11608.1200
1
The aim of this research is to apply the stochastic arithmetic (SA) for validating the Sinccollocation method (SCM) with single or double exponentially decay to find the numerical solution of second kind Fredholm integral equation (IE). To this end, the CESTAC(Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library are applied. Using this method, the optimal iteration of SCM, the optimal approximation, the absolute error and the numerical instabilities can be determined. A theorem is proved which shows the accuracy of the SCM by means of the concept of common significant digits. Some IEs are presented and the numerical results of comparison between the single exponentially decay (SE) and the double exponentially decay (DE) are demonstrated in the tables.
0

63
84


Mohammad Ali
Fariborzi
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Iran
m_fariborzi@iauctb.ac.ir


Samad
Noeiaghdam
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Iran
s.noeiaghdam.sci@iauctb.ac.ir
Stochastic arithmetic
CESTAC
Sinccollocation method
CADNA library
Single exponentially decay
Double exponentially decay
Fredholm integral equations
1

Solving a timefractional inverse heat conduction problem with an unknown nonlinear boundary condition
https://jmm.guilan.ac.ir/article_3192.html
10.22124/jmm.2018.11656.1204
1
In this paper, we consider a timefractional inverse heat conduction problem with an unknown function in the nonlinear boundary condition. First, illposedness of this problem is shown. Thus, we will apply the mollification regularization method with Gauss kernel to regularize the problem, then the space marching finite difference method is considered to solve numerically the mollified problem. The generalized crossvalidation choice rule is used to find a suitable regularization parameter. The numerical scheme is completely described and the stability and convergence of the solutions are investigated. Finally, some numerical examples are presented to illustrate the validity and effectiveness of the proposed algorithm.
0

85
106


Afshin
Babaei
Faculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran.
Iran
babaei@umz.ac.ir
Inverse problem
Caputo's fractional derivative
Illposedness
Mollification
convergence Analysis
1

Rationalized Haar wavelet bases to approximate the solution of the first Painlev'e equations
https://jmm.guilan.ac.ir/article_3212.html
10.22124/jmm.2018.11881.1214
1
In this article, using the properties of the rationalized Haar (RH) wavelets and the matrix operator, a method is presented for calculating the numerical approximation of the first Painlev'e equations solution. Also, an upper bound of the error is given and by applying the Banach fixed point theorem the convergence analysis of the method is stated. Furthermore, an algorithm to solve the first Painlev'e equation is proposed. Finally, the reported results are compared with some other methods to show the effectiveness of the proposed approach.
0

107
116


Majid
Erfanian
Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran
Iran
erfaniyan@uoz.ac.ir


Amin
Mansoori
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Iran
amansoori@um.ac.ir
Wave equation
first Painlev'e equation
Volterra integral equation
RH wavelet
1

An economic group model for innovation diffusion of new product with delay of adoption for low income group
https://jmm.guilan.ac.ir/article_3227.html
10.22124/jmm.2018.10330.1155
1
In this paper, an economic group delay model is established. Dynamical behavior and Basic influence number of the proposed system are studied. Asymptotic stability analysis is carried out for the steadystates. The critical value of the delay $tau$ is determined. It is observed that for the interior steadystate remains stable if the adoption delay for the lowincome group is less than the threshold value, i.e., $tau<tau_{0}^+$. If $tau$ crosses its threshold, system perceives oscillating behavior, and Hopf bifurcation occurs. Moreover, sensitivity analysis is performed for the system parameter used in the interior steadystate. Finally, numerical simulations are conducted to support our analytical findings.
0

117
132


Rishi
Tuli
Research Scholar, IKGPunjab Technical University, Kapurthala, India
Iran
tulirishu@gmail.com


Joydip
Dhar
ABVIIITM, Gwalior, M.P., India
Iran
jdhar.iiitmg@gmail.com


Harbax
Bhatti
B.B.S.B. Engineering College, Fatehgarh Sahib Punjab, India
Iran
bhattihs100@yahoo.com
Boundedness
positivity
delay
Hopf bifurcation
sensitivity analysis
1

A nonlocal Cauchy problem for nonlinear fractional integrodifferential equations with positive constant coefficient
https://jmm.guilan.ac.ir/article_3342.html
10.22124/jmm.2019.11580.1199
1
In this paper, we study the existence, uniqueness and stability of solutions of a nonlocal Cauchy problem for nonlinear fractional integrodifferential equations with positive constant coefficient. The results heavily depend on the Banach contraction principle, Schaefer's fixed point theorem and Pachpatte's integral inequality. In the last, results are illustrated with suitable example.
0

133
151


Shivaji Ramchandra
Tate
Department of Mathematics, Kisan Veer Mahavidyalaya, Wai, India
Iran
tateshivaji@gmail.com


Vinod Vijaykumar
Kharat
Department of Mathematics, N.B. Navale Sinhgad College of Engg., Solapur, India
Iran
vvkvinod9@gmail.com


Hambirrao Tatyasaheb
Dinde
Department of Mathematics, Karmaveer Bhaurao Patil College,UrunIslampur, India
Iran
drhtdmaths@gmail.com
Fractional integrodifferential equation
Existence of solution
Fixed point
Pachpatte's integral inequality
Stability