J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.9220.1136 Research Paper Existence and continuation of solutions of Hilfer fractional differential equations Existence and continuation of solutions of Hilfer FDEs Bhairat Sandeep P. Department of mathematics, Institute of Chemical Technology, Mumbai--400 019 (M.S.), India 01 03 2019 7 1 1 20 07 12 2017 14 10 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3048.html

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.

Fractional differential equations local existence continuation theorem global solutions
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.11242.1189 Research Paper Bases for polynomial-based spaces Bases for polynomial-based spaces Mohammadi Maryam Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran Bahrkazemi Maryam School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran 01 03 2019 7 1 21 34 08 09 2018 14 10 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3049.html

Since it is well-known that the Vandermonde matrix is ill-conditioned, this paper surveys the choices of other bases. These bases are data-dependent 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.

Polynomial interpolation interpolation bases monomial bases duality Vandermonde matrix Gramian Matrix matrix decomposition
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.9994.1148 Research Paper A new two-parameter distribution: properties and applications A new two-parameter distribution: properties and applications Abdollahi Nanvapisheh Anita Department of Statistics, Islamic Azad University, Tehran north branch, Tehran, Iran MirMostafaee S.M.T.K. Department of Statistics, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran Altun Emrah Department of Statistics, Bartin University, Bartin 74100, Turkey 01 03 2019 7 1 35 48 17 03 2018 28 11 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3102.html

In this paper, a new two-parameter lifetime distribution called ``the exponentiated Shanker distribution" is suggested. The new distribution has an increasing, decreasing and bathtub-shaped 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.

Exponentiated Shanker distribution goodness of fit lifetime data mathematical and statistical characteristics parameter estimation
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.10117.1153 Research Paper Global dynamics of a mathematical model on smoking: impact of anti-smoking campaign Global Dynamics of a Mathematical Model on Smoking: Impact of anti-Smoking Campaign Verma Vinay Department of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki-225003, India Bhadauria Archana Department of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki-225003, India 01 03 2019 7 1 49 62 18 04 2018 13 10 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3187.html

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 smoking-free equilibrium is stable when a threshold, termed as the smokers-generation 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.

Smoking Education media global Stability Lyapunov function
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.11608.1200 Research Paper Valid implementation of the Sinc-collocation method to solve linear integral equations by the CADNA library Valid implementation of the Sinc-collocation method Fariborzi Mohammad Ali Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. Noeiaghdam Samad Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. 01 03 2019 7 1 63 84 30 10 2018 28 12 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3191.html

The aim of this research is to apply the stochastic arithmetic (SA) for validating the Sinc-collocation method (S-CM) 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 S-CM, the optimal approximation, the absolute error and the numerical instabilities can be determined. A theorem is proved which shows the accuracy of the S-CM 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.

Stochastic arithmetic CESTAC Sinc-collocation method CADNA library Single exponentially decay Double exponentially decay Fredholm integral equations
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.11656.1204 Research Paper Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition Babaei Afshin Faculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran. 01 03 2019 7 1 85 106 09 11 2018 29 12 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3192.html

In this paper, we consider a time-fractional inverse heat conduction problem with an unknown function in the nonlinear boundary condition. First, ill-posedness 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 cross-validation 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.

Inverse problem Caputo's fractional derivative Ill-posedness Mollification convergence Analysis
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.11881.1214 Research Paper Rationalized Haar wavelet bases to approximate the solution of the first Painlev'e equations Approximate the solution of the first Painlev'e equations Erfanian Majid Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran Mansoori Amin Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran 01 03 2019 7 1 107 116 04 12 2018 28 12 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3212.html

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.

Wave equation first Painlev'e equation Volterra integral equation RH wavelet
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.10330.1155 Research Paper An economic group model for innovation diffusion of new product with delay of adoption for low income group An economic group model for innovation diffusion of new product with delay of adoption for low income group Tuli Rishi Research Scholar, IKG-Punjab Technical University, Kapurthala, India Dhar Joydip ABV-IIITM, Gwalior, M.P., India Bhatti Harbax B.B.S.B. Engineering College, Fatehgarh Sahib Punjab, India 01 03 2019 7 1 117 132 10 05 2018 04 12 2018 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3227.html

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 steady-states. The critical value of the delay \$tau\$ is determined. It is observed that for the interior steady-state remains stable if the adoption delay for the low-income 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 steady-state. Finally, numerical simulations are conducted to support our analytical findings.

Boundedness positivity delay Hopf bifurcation sensitivity analysis
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2019.11580.1199 Research Paper A nonlocal Cauchy problem for nonlinear fractional integro-differential equations with positive constant coefficient A Nonlocal Cauchy Problem for Nonlinear Fractional Integro-Differential Equations with Positive Constant Coefficient Tate Shivaji Ramchandra Department of Mathematics, Kisan Veer Mahavidyalaya, Wai, India Kharat Vinod Vijaykumar Department of Mathematics, N.B. Navale Sinhgad College of Engg., Solapur, India Dinde Hambirrao Tatyasaheb Department of Mathematics, Karmaveer Bhaurao Patil College,Urun--Islampur, India 01 03 2019 7 1 133 151 05 11 2018 21 01 2019 Copyright © 2019, دانشگاه گیلان. 2019 https://jmm.guilan.ac.ir/article_3342.html

In this paper, we study the existence, uniqueness and stability of solutions of a nonlocal Cauchy problem for nonlinear fractional integro-differential 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.

Fractional integro-differential equation Existence of solution Fixed point Pachpatte&#039;s integral inequality Stability