ORIGINAL_ARTICLE Existence and continuation of solutions of Hilfer fractional differential equations 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. https://jmm.guilan.ac.ir/article_3048_5abfe4f6dc0a6ad18e139b42b6c1c26c.pdf 2019-03-01 1 20 10.22124/jmm.2018.9220.1136 Fractional differential equations local existence continuation theorem global solutions Sandeep P. Bhairat sp.bhairat@ictmumbai.edu.in 1 Department of mathematics, Institute of Chemical Technology, Mumbai--400 019 (M.S.), India LEAD_AUTHOR
ORIGINAL_ARTICLE Bases for polynomial-based spaces 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. https://jmm.guilan.ac.ir/article_3049_690e13a27bd207112d0b5f88eabeeaaa.pdf 2019-03-01 21 34 10.22124/jmm.2018.11242.1189 Polynomial interpolation interpolation bases monomial bases duality Vandermonde matrix Gramian Matrix matrix decomposition Maryam Mohammadi m.mohammadi@khu.ac.ir 1 Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran LEAD_AUTHOR Maryam Bahrkazemi m.bahrkazemi@alumni.iust.ac.ir 2 School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran AUTHOR
ORIGINAL_ARTICLE A new two-parameter distribution: properties and applications 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. https://jmm.guilan.ac.ir/article_3102_56053ebfad91c8335d246d109bf34e11.pdf 2019-03-01 35 48 10.22124/jmm.2018.9994.1148 Exponentiated Shanker distribution goodness of fit lifetime data mathematical and statistical characteristics parameter estimation Anita Abdollahi Nanvapisheh anita.abdollahi@yahoo.com 1 Department of Statistics, Islamic Azad University, Tehran north branch, Tehran, Iran LEAD_AUTHOR S.M.T.K. MirMostafaee m.mirmostafaee@umz.ac.ir 2 Department of Statistics, University of Mazandaran, P.O. Box 47416-1467, Babolsar, Iran AUTHOR Emrah Altun emrahaltun@bartin.edu.tr 3 Department of Statistics, Bartin University, Bartin 74100, Turkey AUTHOR
ORIGINAL_ARTICLE Global dynamics of a mathematical model on smoking: impact of anti-smoking campaign 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. https://jmm.guilan.ac.ir/article_3187_377e2a6014896f5eb6b57a6be96d189f.pdf 2019-03-01 49 62 10.22124/jmm.2018.10117.1153 Smoking Education media global Stability Lyapunov function Vinay Verma vinay.verma09@rediffmail.com 1 Department of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki-225003, India LEAD_AUTHOR Archana Bhadauria archanasingh93@yahoo.co.in 2 Department of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki-225003, India AUTHOR
ORIGINAL_ARTICLE Valid implementation of the Sinc-collocation method to solve linear integral equations by the CADNA library 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. https://jmm.guilan.ac.ir/article_3191_7f0189af9b25b9010b1030de4b7b8035.pdf 2019-03-01 63 84 10.22124/jmm.2018.11608.1200 Stochastic arithmetic CESTAC Sinc-collocation method CADNA library Single exponentially decay Double exponentially decay Fredholm integral equations Mohammad Ali Fariborzi m_fariborzi@iauctb.ac.ir 1 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. LEAD_AUTHOR Samad Noeiaghdam s.noeiaghdam.sci@iauctb.ac.ir 2 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran. AUTHOR
ORIGINAL_ARTICLE Solving a time-fractional inverse heat conduction problem with an unknown nonlinear boundary condition 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. https://jmm.guilan.ac.ir/article_3192_d0e202976070aee9a670630923af2f0b.pdf 2019-03-01 85 106 10.22124/jmm.2018.11656.1204 Inverse problem Caputo's fractional derivative Ill-posedness Mollification convergence Analysis Afshin Babaei babaei@umz.ac.ir 1 Faculty of MAthematical sciences, University of Mazandaran, Babolsar, Iran. LEAD_AUTHOR
ORIGINAL_ARTICLE Rationalized Haar wavelet bases to approximate the solution of the first Painlev'e equations 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. https://jmm.guilan.ac.ir/article_3212_4abf5373c41b9ab6b4ccd79694cdc8c3.pdf 2019-03-01 107 116 10.22124/jmm.2018.11881.1214 Wave equation first Painlev'e equation Volterra integral equation RH wavelet Majid Erfanian erfaniyan@uoz.ac.ir 1 Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran LEAD_AUTHOR Amin Mansoori a-mansoori@um.ac.ir 2 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran AUTHOR
ORIGINAL_ARTICLE An economic group model for innovation diffusion of new product with delay of adoption for low income group 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. https://jmm.guilan.ac.ir/article_3227_1bfc83f2c2dba775c2891c5288d2eb59.pdf 2019-03-01 117 132 10.22124/jmm.2018.10330.1155 Boundedness positivity delay Hopf bifurcation sensitivity analysis Rishi Tuli tulirishu@gmail.com 1 Research Scholar, IKG-Punjab Technical University, Kapurthala, India LEAD_AUTHOR Joydip Dhar jdhar.iiitmg@gmail.com 2 ABV-IIITM, Gwalior, M.P., India AUTHOR Harbax Bhatti bhattihs100@yahoo.com 3 B.B.S.B. Engineering College, Fatehgarh Sahib Punjab, India AUTHOR
ORIGINAL_ARTICLE A nonlocal Cauchy problem for nonlinear fractional integro-differential equations with positive constant coefficient 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. https://jmm.guilan.ac.ir/article_3342_72bd29e2068c0e2b41eb06371560d3c2.pdf 2019-03-01 133 151 10.22124/jmm.2019.11580.1199 Fractional integro-differential equation Existence of solution Fixed point Pachpatte&#039;s integral inequality Stability Shivaji Ramchandra Tate tateshivaji@gmail.com 1 Department of Mathematics, Kisan Veer Mahavidyalaya, Wai, India LEAD_AUTHOR Vinod Vijaykumar Kharat vvkvinod9@gmail.com 2 Department of Mathematics, N.B. Navale Sinhgad College of Engg., Solapur, India AUTHOR Hambirrao Tatyasaheb Dinde drhtdmaths@gmail.com 3 Department of Mathematics, Karmaveer Bhaurao Patil College,Urun--Islampur, India AUTHOR