novel inequalities for generalized graph entropies graph energies and topological indices the entropy of a graph is an information theoretic quantity for measuring the complexity of a graph after shannon introduced the entropy to information and communication many generalizations of the entropy measure have been proposed such as renyi entropy and daroczy entropy in this article we prove accurate connections inequalities between generalized graph entropies graph energies and topological indices additionally we obtain some extremal properties of nine generalized graph entropies by employing graph energies and topological indices

the effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking stretching sheet the effects of variable viscosity and thermal conductivity on the flow and heat transfer in a laminar liquid film on a horizontal shrinking stretching sheet are analyzed the similarity transformation reduces the time independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations the resulting five parameter problem is solved by the homotopy perturbation method the results are presented graphically to interpret various physical parameters appearing in the problem

maximum laplacian energy among threshold graphs we impose some restrictions on the spectra of a threshold graph allowing us to compute its laplacian energy we then show that the pineapple with clique number 1 2n3 has largest laplacian energy among all pineapples with n vertices and among all the graphs satisfying those conditions we also find large families of threshold graphs that satisfy those restrictions and exhibit pairs of such graphs with the same laplacian energy and different laplacian spectra we show by computation that the above pineapple has maximum laplacian energy among all connected threshold graphs for all n 35

investigation of the logarithmic kdv equation involving mittag leffler type kernel with atangana baleanu derivative abstract this work presents analysis of the logarithmic kdv equation involving new fractional operator called atangana baleanu ab fractional derivative with mittag leffler ml type kernel the existence and uniqueness of the governing equation having ab fractional derivative with ml type kernel is proved with the aid of a fixed point theorem we present numerical simulations by using iterative algorithm the effectiveness of various parameters and variables on the displacement are presented in figures 1 and 2

extended framework of hamilton s principle applied to duffing oscillation abstract the paper begins with a novel variational formulation of duffing equation using the extended framework of hamilton s principle ehp unlike the original hamilton s principle this formulation properly accounts for initial conditions and it recovers all the governing differential equations as its euler lagrange equation thus it serves base for the development of novel computational methods involving finite element representation over time for its feasibility we provide the simplest temporal finite element method by adopting linear temporal shape functions numerical examples are included to verify and investigate performance of non iterative algorithm in the developed method

a comparative study on the analytic solutions of fractional coupled sine gordon equations by using two reliable methods new modified homotopy analysis method has been proposed the proposed novel method is well suited for present fractional s g equation it is obvious to see that the mham is more accurate easy and efficient than hptm fractional coupled s g equations have been first time solved by mham and hptm in this paper modified homotopy analysis method mham and homotopy perturbation transform method hptm have been implemented for solving time fractional coupled sine gordon equations we consider fractional coupled sine gordon equations which models one dimensional nonlinear wave processes in two component media the results obtained by modified homotopy analysis method mham and homotopy perturbation transform method hptm are then compared with the modified decomposition method mdm by using an initial value system the numerical solutions of coupled sine gordon equations have been represented graphically here we obtain the solution of fractional coupled sine gordon s g equations which is obtained by replacing the time derivatives with a fractional derivatives of order 1 2 and 1 2 the fractional derivatives here are described in caputo sense

solving random mixed heat problems this paper develops a random mean square fourier transform approach to solve random partial differential heat problems with nonhomogeneous boundary value conditions random mean square operational rules for the random fourier sine and cosine transforms are stated and illustrative examples are included

randic energy of specific graphs let g be a simple graph with vertex set v g v 1 v 2 v n the randic matrix of g denoted by r g is defined as the n n matrix whose i j entry is d i d j 1 2 if vi and vj are adjacent and 0 for another cases let the eigenvalues of the randic matrix r g be 1 2 n which are the roots of the randic characteristic polynomial i 1 n i the randic energy re of g is the sum of absolute values of the eigenvalues of r g in this paper we compute the randic characteristic polynomial and the randic energy for specific graphs

analytical and numerical solutions of a nonlinear alcoholism model via variable order fractional differential equations abstract in this paper we analyze an alcoholism model which involves the impact of twitter via liouville caputo and atangana baleanu caputo fractional derivatives with constant and variable order two fractional mathematical models are considered with and without delay special solutions using an iterative scheme via laplace and sumudu transform were obtained we studied the uniqueness and existence of the solutions employing the fixed point postulate the generalized model with variable order was solved numerically via the adams method and the adams bashforth moulton scheme stability and convergence of the numerical solutions were presented in details numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient therefore by including both the fractional derivatives and finite time delays in the alcoholism model studied we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking

he s homotopy perturbation method for a boundary layer equation in unbounded domain by means of he s homotopy perturbation method hpm an approximate solution of a boundary layer equation in unbounded domain is obtained comparison is made between the obtained results and those in open literature the results show that the method is very effective and simple

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

a new modification of the variational iteration method this paper presents a new variational iteration algorithm which provides great freedom in choosing linear operators for various nonlinear equations so that the lagrange multiplier can be effectively identified

multiple front solutions for the burgers kadomtsev petviashvili equation abstract in this work we study a completely integrable dissipative equation the burgers equation is extended by using the sense of the kadomtsev petviashvili kp equation the new established burgers kp equation is studied by using the tanh coth method to obtain kink solutions and periodic solutions we also apply the powerful hirota s bilinear method to establish exact n soliton solutions for the derived integrable equation

on the laplacian energy like invariant abstract let g be a connected graph of order n with laplacian eigenvalues 1 2 n 1 n 0 the laplacian energy like invariant of the graph g is defined as lel lel g i 1 n 1 i lower and upper bounds for lel are obtained in terms of n number of edges maximum vertex degree and number of spanning trees

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

degree maximal graphs are laplacian integral abstract an integer sequence d d 1 d 2 d n is graphic if there is a graph whose degree sequence is d a graph g is maximal if its degree sequence is majorized by no other graphic sequence the laplacian matrix of g is l g d g a g where d g is the diagonal matrix of vertex degrees and a g is the 0 1 adjacency matrix the article contains an explicit algorithmic construction of all maximal graphs from which it follows e g that apart from 0 the laplacian spectrum of a maximal graph is the conjugate of its degree sequence

on the sum of the laplacian eigenvalues of a tree given an n vertex graph g v e the laplacian spectrum of g is the set of eigenvalues of the laplacian matrix l d a where d and a denote the diagonal matrix of vertex degrees and the adjacency matrix of g respectively in this paper we study the laplacian spectrum of trees more precisely we find a new upper bound on the sum of the k largest laplacian eigenvalues of every n vertex tree where k 1 n this result is used to establish that the n vertex star has the highest laplacian energy over all n vertex trees which answers affirmatively to a question raised by radenkovic and gutman 10

solitons and discrete eigenfunctions of the recursion operator of non linear evolution equations i the caudrey dodd gibbon sawada kotera equation the solution of the third order isospectral equation of the caudrey dodd gibbon sawada kotera equation cdgske for soliton potential is obtained recursively from the riccati equation derived by iterating once the auto backlund transformation it is then shown that the discrete eigenfunctions of the sixth order recursion operator for this equation can be written in terms of the solutions of the isospectral equation the behaviour of the 1 soliton solution which has certain novel features is studied a sine gordon like equation resembling the double sine gordon equation is derived from the cdgske

on the tree with diameter 4 and maximal energy the energy of a simple graph is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix jianping found the structure of trees which have maximal energy among all trees of diameter 4 whose centers are of degree t this paper generalizes the result we determine the structure of the general tree of diameter 4 and maximal energy

exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method the purpose of this study is to introduce a modification of the homotopy perturbation method using laplace transform and pade approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations two test examples are given the coupled nonlinear system of burger equations and the coupled nonlinear system in one dimensional thermoelasticity the results obtained ensure that this modification is capable of solving a large number of nonlinear differential equations that have wide application in physics and engineering

extremal laplacian energy of threshold graphs let g be a connected threshold graph of order n with m edges and trace t in this paper we give a lower bound on laplacian energy in terms of n m and t of g from this we determine the threshold graphs with the first four minimal laplacian energies moreover we obtain the threshold graphs with the largest and the second largest laplacian energies

spectral properties of geometric arithmetic index the concept of geometric arithmetic index was introduced in the chemical graph theory recently but it has shown to be useful one of the main aims of algebraic graph theory is to determine how or whether properties of graphs are reflected in the algebraic properties of some matrices the aim of this paper is to study the geometric arithmetic index ga1 from an algebraic viewpoint since this index is related to the degree of the vertices of the graph our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices moreover using this matrix we define a ga laplacian matrix which determines the geometric arithmetic index of a graph and satisfies properties similar to the ones of the classical laplacian matrix

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

symbolic computation and new families of exact soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces in this paper new families of soliton like solutions are obtained for 2 1 dimensional integrable broer kaup equations by using the symbolic computation method developed by gao and tian sample solutions obtained from these methods are presented solitary wave solutions are merely a special case in one family the method can also be extended to other types of nonlinear evolution equations in mathematical physics

mean square solution of bessel differential equation with uncertainties this paper deals with the study of a bessel type differential equation where input parameters coefficient and initial conditions are assumed to be random variables using the so called l p random calculus and assuming moment conditions on the random variables in the equation a mean square convergent generalized power series solution is constructed as a result of this convergence the sequences of the mean and standard deviation obtained from the truncated power series solution are convergent as well the results obtained in the random framework extend their deterministic counterpart the theory is illustrated in two examples in which several distributions on the random inputs are assumed finally we show through examples that the proposed method is computationally faster than monte carlo method

analytical study of fractional bratu type equation arising in electro spun organic nanofibers elaboration abstract in this article we present a hybrid analytical scheme namely homotopy perturbation transform method to achieve the solutions of the non linear bratu type problem with fractional order derivatives the caputo type fractional derivatives are considered in the present article he s polynomial is used to tackle the nonlinearity which arise in our considered problem using the initial conditions the numerical solutions of the problem are computed the numerical procedure reveals that only a few iterations are needed for better approximation of the solutions which illustrates the effectiveness and reliability of the method effects of fractional order derivatives on the solutions for various particular cases are depicted through graphs

the homotopy perturbation method for nonlinear oscillators with discontinuities in the paper the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities only one iteration leads to high accuracy of the solutions

the bi hamiltonian structure of some nonlinear fifth and seventh order differential equations and recursion formulas for their symmetries and conserved covariants using a bi hamiltonian formulation we give explicit formulas for the conserved quantities and infinitesimal generators of symmetries for some nonlinear fifth and seventh order nonlinear partial differential equations among them the caudrey dodd gibbon sawada kotera equation and the kupershmidt equation we show that the lie algebras of the symmetry groups of these equations are of a very special form among the c vector fields they are generated from two given commuting vector fields by a recursive application of a single operator furthermore for some higher order equations those multisoliton solutions which for t asymptotically decompose into traveling wave solutions are characterized as eigenvector decompositions of certain operators

solution of physical problems by decomposition recent generalizations are discussed and results are presented for the theory and applications of the decomposition method application is made to the duffing equation with an error of 0 0001 in only four terms and less than 10 16 in thirteen terms of the decomposition series application is also made to a dissipative wave equation a matrix riccati equation and advection diffusion nonlinear transport

a comparison between the variational iteration method and adomian decomposition method in this paper we present a comparative study between the variational iteration method and adomian decomposition method the study outlines the significant features of the two methods the analysis will be illustrated by investigating the homogeneous and the nonhomogeneous advection problems

global dynamics of vector borne diseases with horizontal transmission in host population the paper presents the dynamical features of a vector host epidemic model with direct transmission first we extended the model by taking into account the exposed individuals in both human and vector population with the impact of disease related deaths and total time dependent population size using lyapunov function theory some sufficient conditions for global stability of both the disease free equilibrium and the endemic equilibrium are obtained for the basic reproductive number r 0 1 a unique endemic equilibrium exists and is globally asymptotically stable furthermore it is found that the model exhibits the phenomenon of backward bifurcation where the stable disease free equilibria coexists with a stable endemic equilibrium finally numerical simulations are carried out to investigate the influence of the key parameters on the spread of the vector borne disease to support the analytical conclusion and illustrate possible behavioral scenarios of the model

modified laplace variational iteration method for solving fourth order parabolic partial differential equation with variable coefficients abstract in the present study a new amendment in laplace variational iteration method for the solution of fourth order parabolic partial differential equations with variable coefficients is revealed i e modified laplace variational iteration method ml vim the proposed modification is made by coupling of two methods one of them is variational iteration method vim and the other one is laplace transformation lt our modification has an important beauty that one has no need to compute lagrange multiplier via integration nor by taking convolution theorem and has a simple way to use in the implementation of our proposed scheme moreover homotopy perturbation method hpm with he s polynomials is employed for the computation of nonlinear terms the main improvement of our proposed scheme is the reduction of the problem to a simple one which also embraces for solving a nonlinear term some illustrated examples are interpreted which unveil the robustness and accuracy of the newly developed scheme

theory and application for the system of fractional burger equations with mittag leffler kernel abstract in this work the system of fractional burger differential equations are presented as a new fractional model for atangana baleanu fractional derivative with mittag leffler kernel the approximate consequences are analysed by applying an recurrent process the existence and uniquenes of solution for this system is discussed in order to appear the effects of several parameter and variables on the movement the approximate results are showed in graphics and are compared with obtained solutions for two different derivative in tables

on the combinatorics of the hirota d operators a generic formula is presented which relates the hirota d operators to simple combinatorics particular classes of partition polynomials bell polynomials and generalizations are found to play an important role in the characterization of bilinearizable equations as a consequence it is shown that bilinear backlund transformations for single field bilinearizable equations linearize systematically into corresponding laxpairs

on classes of integrable systems and the painleve property the caudrey dodd gibbon equation is found to possess the painleve property investigation of the backlund transformations for this equation obtains the kuperschmidt equation a certain transformation between the kuperschmidt and caudrey dodd gibbon equation is obtained this transformation is employed to define a class of p d e s that identically possesses the painleve property for equations within this class backlund transformations and rational solutions are investigated in particular the sequences of higher order kdv caudrey dobb gibbon and kuperschmidt equations are shown to possess the painleve property

fractional variational iteration method for fractional initial boundary value problems arising in the application of nonlinear science in this paper we suggest a fractional functional for the variational iteration method to solve the linear and nonlinear fractional order partial differential equations with fractional order initial and boundary conditions by using the modified riemann liouville fractional derivative proposed by g jumarie fractional order lagrange multiplier has been considered solution has been plotted for different values of a

delta dressing and exact solutions for the 2 1 dimensional harry dym equation exact implicit solutions with functional parameters of the 2 1 dimensional harry dym hd equation are constructed by the delta dressing method the interrelation between the hd and modified kadomtsev petviashvili mkp equations is established within the framework of the delta dressing method knowledge of the mkp eigenfunctions allows the solutions of the 2 1 dimensional hd equation to be represented in a simple parametric form

n soliton solutions for the combined kdv cdg equation and the kdv lax equation abstract the hirota ito approach presented in r hirota m ito resonance of solitons in one dimension j phys soc jpn 52 3 1983 744 748 for extending fifth order integrable equations with a nonvanishing boundary conditions to combined equations is used in this work the generalized fifth order caudrey dodd gibbon cdg and lax equations are extended to combined integrable equations the hirota s bilinear method is used to derive multiple soliton solutions for the extended kdv cdg and kdv lax equations

numerical solution of duffing equation by the laplace decomposition algorithm the laplace decomposition algorithm lda is a numerical algorithm can be adapted to solve duffing equations this paper both describes the principle of lda and discusses its advantages and drawbacks concrete example are also studied to show with numerical results how the lda works efficiently

he s homotopy perturbation method an effective tool for solving nonlinear integral and integro differential equations in this paper we conduct a comparative study among he s homotopy perturbation method and three traditional methods for an analytic and approximate treatment of nonlinear integral and integro differential equations the proper implementation of he s homotopy perturbation method can extremely minimize the size of work if compared to existing traditional techniques the analysis is accompanied by examples that demonstrate the comparison and shows the pertinent features of the homotopy perturbation technique

backlund transformation lax pair and solutions for the caudrey dodd gibbon equation by using bell polynomials and symbolic computation we investigate the caudrey dodd gibbon equation analytically through a generalization of bells polynomials its bilinear form is derived based on which the periodic wave solution and soliton solutions are presented and the soliton solutions with graphic analysis are also given furthermore backlund transformation and lax pair are derived via the bells exponential polynomials finally the ablowitz kaup newell segur system is constructed

on the solutions of fractional swift hohenberg equation with dispersion in this article the approximate solutions of the non linear swift hohenberg equation with fractional time derivative in the presence of dispersive term have been obtained the fractional derivative is described in caputo sense time fractional nonlinear partial differential equations in the presence of dispersion and bifurcation parameters have been computed numerically to predict hydrodynamic fluctuations at convective instability for different particular cases and results are depicted through graphs

the inertia and energy of the distance matrix of a connected graph abstract let g be a connected graph and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalues of g in this paper we show that the distance matrix of a clique tree is non singular moreover we also prove that the distance matrix of a clique tree has exactly one positive d eigenvalue in addition we determine the extremal graphs with maximum and minimum distance energy among all clique trees

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

analysis of regularized long wave equation associated with a new fractional operator with mittag leffler type kernel abstract in this work we aim to present a new fractional extension of regularized long wave equation the regularized long wave equation is a very important mathematical model in physical sciences which unfolds the nature of shallow water waves and ion acoustic plasma waves the existence and uniqueness of the solution of the regularized long wave equation associated with atangana baleanu fractional derivative having mittag leffler type kernel is verified by implementing the fixed point theorem the numerical results are derived with the help of an iterative algorithm in order to show the effects of various parameters and variables on the displacement the numerical results are presented in graphical and tabular form

weighted finite difference techniques for the one dimensional advection diffusion equation various numerical techniques will be developed and compared for solving the one dimensional advection diffusion equation with constant coefficient these techniques are based on the two level finite difference approximations the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the new methods are more accurate and are more efficient than the conventional techniques these schemes are free of numerical diffusion the results of a numerical experiment are presented and the accuracy and central processor cpu time needed are discussed and compared

asymptotic laplacian energy like invariant of lattices let 1 2 n denote the laplacian eigenvalues of a graph g with n vertices the laplacian energy like invariant denoted by lel g i 1 n 1 i is a novel topological index in this paper we show that the laplacian energy like per vertex of various lattices is independent of the toroidal cylindrical and free boundary conditions simultaneously the explicit asymptotic values of the laplacian energy like in these lattices are obtained moreover our approach implies that in general the laplacian energy like per vertex of other lattices is independent of the boundary conditions

inner resonance of a coupled hyperbolic tangent nonlinear oscillator arising in a packaging system abstract in this paper a dynamic model of a coupled hyperbolic tangent nonlinear oscillator arising in a packaging system is proposed conditions for resonance are obtained by applying the variational iteration method ii vim ii which should be avoided in the cushioning packaging design moreover the comparison between the vim ii and numerical solutions indicates an excellent agreement

multiple soliton solutions for the kp equation by hirota s bilinear method and by the tanh coth method abstract in this work we use the hirota s direct method combined with the simplified version of this method to determine the n soliton solutions n 1 2 3 4 5 for the kadomtsev petviashvili kp equation the one soliton solutions will be handled by the tanh coth method the work emphasizes the power of the two methods that will be used

comparison of homotopy perturbation method and homotopy analysis method comparison of homotopy perturbation method hpm and homotopy analysis method is made revealing that the former is more powerful than the later furthermore the hpm is further developed in this paper by applying the modern perturbation methods

convergence and error estimation of homotopy perturbation method for fredholm and volterra integral equations abstract in this paper an application of the homotopy perturbation method for solving fredholm and volterra integral equations of the second kind is presented discussed method consists in constructing the functional series sum of which determines the function giving the solution of considered problem conditions under which the constructed series is convergent are formulated and proved in the paper in general the composed series is rather fast convergent thanks to which calculation of few first terms ensures a very good approximation of the sought solution estimation of errors of approximate solution obtained by taking the partial sum of the series is also elaborated in the paper

extracting a general iterative method from an adomian decomposition method and comparing it to the variational iteration method in this work a new form of adomian decomposition method adm is presented by this form a general iterative method can be achieved in which there is no need of calculating adomian polynomials also this general iterative method is compared with the adomian decomposition method and variational iteration method vim and its advantages are expressed

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method