University of KashanIranian Journal of Mathematical Chemistry2228-64898420171201Borderenergetic Graphs of Order 123393444978810.22052/ijmc.2017.87093.1290ENB.FurtulaFaculty of Science, University of Kragujevac, Serbia.I.GutmanFaculty of Science, University of Kragujevac, Kragujevac, SerbiaJournal Article20170523A graph G of order n is said to be borderenergetic if its energy is equal to 2n-2 and if G differs from the complete graph Kn. The first such graph was discovered in 2001, but their systematic study started only in 2015. Until now, the number of borderenergetic graphs of order n was determined for nhttps://ijmc.kashanu.ac.ir/article_49788_59c1216a190db25eecedafc58a8b0ef3.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898420171201A Numerical Study of Fractional Order Reverse Osmosis Desalination Model using Legendre Wavelet Approximation3453644803210.22052/ijmc.2017.86494.1289ENO.BelhamitiDepartment of Mathematics and Computer Science
Faculty of Science and Computer Science
University of Mostaganem
Mostaganem
AlgeriaB.AbsarDepartment of Chemical Processes
Faculty of Engineering
Abdelhamid Ibn Badis University,
Mostaganem, AlgeriaJournal Article20170520The purpose of this study is to develop a new approach in modeling and simulation of a reverse osmosis desalination system by using fractional differential equations. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. Examples are developed to illustrate the fractional differential technique and to highlight the broad applicability and the efficiency of this method. The fractional derivative is described in the Caputo sense.https://ijmc.kashanu.ac.ir/article_48032_353840879c192f585d7f14d06d947d30.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898420171201Solving Time-fractional Chemical Engineering Equations by Modified Variational Iteration Method as Fixed Point Iteration Method3653754535110.22052/ijmc.2017.29095.1109ENA.HaghbinIslamic Azad University, GorganH.JafariUniversity of MazandaranJournal Article20150518The variational iteration method(VIM) was extended to find approximate solutions of<br /> fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The obtained approximate solutions are compared with the numerical results in the literature to show the applicability, efficiency and accuracy of the method.https://ijmc.kashanu.ac.ir/article_45351_663180f12cd27ea2d0147431b6a81d9b.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898420171201The Ratio and Product of the Multiplicative Zagreb Indices3773904511610.22052/ijmc.2017.53731.1198ENR.KazemiImam Khomeini international universityJournal Article20160509The first multiplicative Zagreb index $\Pi_1(G)$ is equal to the product of squares of the degree of the vertices and the second multiplicative Zagreb index $\Pi_2(G)$ is equal to the product of<br /> the products of the degree of pairs of adjacent vertices of the underlying molecular graphs $G$. Also, the multiplicative sum Zagreb index $\Pi_3(G)$ is equal to the product of the sums of the degree of pairs of adjacent vertices of $G$. In this paper, we introduce a new version of the multiplicative sum Zagreb index and study the moments of the ratio and product of all above indices in a randomly chosen molecular graph with tree structure of order $n$. Also, a supermartingale is introduced by Doob's supermartingale inequality.https://ijmc.kashanu.ac.ir/article_45116_c080bfbf95b3706d865e19550282e4e3.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898420171201Extremal Trees with Respect to Some Versions of Zagreb Indices Via Majorization3914014864210.22052/ijmc.2017.46693.1161ENM.EliasiDepartment of Mathematics, Khansar Faculty of Computer and Mathematical Sciences, Khansar IranA.GhalavandDepartment of Mathematics, Khansar Faculty of Computer and Mathematical Sciences, Khansar IranJournal Article20160111The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12.https://ijmc.kashanu.ac.ir/article_48642_64062001663bd96ec4ae467dcd11a0d2.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898420171201The Uniqueness Theorem for Inverse Nodal Problems with a Chemical Potential4034113922810.22052/ijmc.2016.39228ENS.MosazadehDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
University of KashanJournal Article20160203In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.https://ijmc.kashanu.ac.ir/article_39228_bffea15fb4cc1335d35422de04f8bfc3.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898420171201Numerical Modeling for Nonlinear Biochemical Reaction Networks4134235001610.22052/ijmc.2017.47506.1170ENZ. A.ZafarLecturer, Department of Computer Science, University of Central Punjab, Lahore, Pakistan.K.RehanAssistant Professor, Department of Mathematics, University of Engineering & Technology, KSK Campus, PakistanM.MushtaqProfessor, University of Engineering and Technology, Lahore Campus, Lahore, Pakistan.M.RafiqAssistant Professor, Faculty of Electrical Engineering, University of Central Punjab, PakistanJournal Article20160126Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A NSFD model has been constructed for the biochemical reaction problem and numerical experiments are performed for different values of discretization parameter ‘h’. The results are compared with the well-known numerical scheme, i.e. RK4. Unlike RK4 which fails for large time steps, the developed scheme gives results that converge to true steady states for any time step used.https://ijmc.kashanu.ac.ir/article_50016_3d4b3705afc3725dcaee76c6dbe32ec1.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64898420171201Numerical Solution of Gas Solution in a Fluid: Fractional Derivative Model4254375003410.22052/ijmc.2017.54560.1203ENS.EsmaeiliDepartment of Applied Mathematics,
University of KurdistanJournal Article20160523A computational technique for solution of mathematical model of gas solution in a fluid is presented. This model describes the change of mass of the gas volume due to diffusion through the contact surface. An appropriate representation of the solution based on the M"{u}ntz polynomials reduces its numerical treatment to the solution of a linear system of algebraic equations. Numerical examples are given and discussed to illustrate the effectiveness of the proposed approach.https://ijmc.kashanu.ac.ir/article_50034_b2a8baae1f6d0082a396ac6810ca2c66.pdf