2017
8
4
0
99
Borderenergetic graphs of order 12
2
2
A graph G of order n is said to be borderenergetic if its energy is equal to 2n2 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 n
1

339
343


B.
Furtula
Faculty of Science, University of Kragujevac, Serbia.
Faculty of Science, University of Kragujevac,
Serbia
furtula@kg.ac.rs


I.
Gutman
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Faculty of Science, University of Kragujevac,
Serbia
gutman@kg.ac.rs
Graph energy
Borderenergetic graph
Spectrum (of graph)
A numerical study of fractional order reverse osmosis desalination model using Legendre wavelet approximation
2
2
The 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 quasilinearization 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.
1

345
364


O.
Belhamiti
Department of Mathematics and Computer Science
Faculty of Science and Computer Science
University of Mostaganem
Mostaganem
Algeria
Department of Mathematics and Computer Science
Fac
Algeria
belhamitio@yahoo.fr


B.
Absar
Department of Chemical Processes
Faculty of Engineering
Abdelhamid Ibn Badis University,
Mostaganem, Algeria
Department of Chemical Processes
Faculty
Algeria
belkacem.absar@univmosta.dz
Reverse osmosis desalination system
Legendre wavelet method
DQL technique
Caputo fractional derivative
Solving timefractional chemical engineering equations by modified variational iteration method as fixed point iteration method
2
2
The variational iteration method(VIM) was extended to find approximate solutions of 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.
1

365
375


A.
Haghbin
Islamic Azad University, Gorgan
Islamic Azad University, Gorgan
I R Iran
ahmadbin@yahoo.com


H.
Jafari
University of Mazandaran
University of Mazandaran
I R Iran
jafari@umz.ac.ir
Fractional differential equations
Variational iteration method
Fixed point theory
Chemical reactor
The ratio and product of the multiplicative Zagreb indices
2
2
The 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 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.
1

377
390


R.
Kazemi
Imam Khomeini international university
Imam Khomeini international university
I R Iran
r.kazemi@sci.ikiu.ac.ir
Molecular graph with tree structure, Multiplicative Zagreb indices
Moments
Doob's supermartingale inequality
Extermal trees with respect to some versions of Zagreb indices via majorization
2
2
The 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
1

391
401


M.
Eliasi
I R Iran
eliasi@math.iut.ac.ir


A.
Ghalavand
Department of Mathematics, Khansar Faculty of Computer and Mathematical Sciences,
Khansar Iran
Department of Mathematics, Khansar Faculty
I R Iran
ali797ghalavand@gmail.com
majorization
General first Zagreb index
Multiplicative Zagreb indices
The uniqueness theorem for inverse nodal problems with a chemical potential
2
2
In this paper, an inverse nodal problem for a secondorder 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.
1

403
411


S.
Mosazadeh
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Kashan
Department of Pure Mathematics,
Faculty of
I R Iran
s.mosazadeh@kashanu.ac.ir
Boundary Value problem
Inverse Nodal problem
Eigenvalues
Nodal points
Numerical modeling for nonlinear biochemical reaction networks
2
2
Nowadays, 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 enzymesubstrate reaction is simulated by the RungeKutta 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 wellknown 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.
1

413
423


Z. A.
Zafar
Lecturer, Department of Computer Science, University of Central Punjab, Lahore, Pakistan.
Lecturer, Department of Computer Science,
Pakistan
zainzafar@ucp.edu.pk


K.
Rehan
Assistant Professor, Department of Mathematics, University of Engineering & Technology, KSK Campus, Pakistan
Assistant Professor, Department of Mathematics,
Pakistan
kkashif.99@gmail.com


M.
Mushtaq
Professor, University of Engineering and Technology, Lahore Campus, Lahore, Pakistan.
Professor, University of Engineering and
Pakistan
mmushtaq@uet.edu.pk


M.
Rafiq
Assistant Professor, Faculty of Electrical Engineering, University of Central Punjab, Pakistan
Assistant Professor, Faculty of Electrical
Pakistan
m.rafiq@ucp.edu.pk
MichaelisMenten model
NSFD Method
RK4 method
Numerical solution of gas solution in a fluid: fractional derivative model
2
2
A 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.
1

425
437


S.
Esmaeili
Department of Applied Mathematics,
University of Kurdistan
Department of Applied Mathematics,
University
I R Iran
sh.esmaeili@uok.ac.ir
Fractional derivatives
Gas solution
M"{u}ntz polynomials
Gaussian quadrature
Collocation method