


The Asymptotic Estimations of the Eigenvalues and Eigenfunctions for the Fourth Order Boundary Value Problem with Smooth Coefficients


Karwan Hama Faraj Jwamer,


Abstract
: 

In this paper, we have an Eigenvalue problem generated by a fourth order differential equation and suitable boundary
conditions which contain a spectral parameter. We obtain asymptotic expressions for the fourth linearly independent solutions, and we
also found new asymptotic formulas for the Eigenvalues and Eigenfunctions of this boundary value problem. 






On Generalized Fractional Order Difference Sequence Spaces Defined by a Sequence of Modulus Functions


Hanan Hasan Sakr,
N. Faried,
M.S.S. Ali,


Abstract
: 

In this paper, we introduce new generalized fractional order difference sequence spaces which are defined by a sequence of modulus functions. Different algebraic and topological properties of these spaces like linearity, completeness and solidity, etc have been studied. Furthermore, we derive necessary and sufficient conditions for the inclusion relations involving these spaces. 






Regional controllability for hyperbolic systems with output constraints


Ali Boutoulout,


Abstract
: 

The aim of this paper is to characterize the minimum energy control that steers a hyperbolic system to a final state between two prescribed functions only on a subregion $\omega$ of the evolution system domain $\Omega$. We give some definitions and properties of this new concept, and then we
concentrate on the determination of the control which would realize a given final state with output constraints in $\omega$ with minimum energy. This problem is solved using the Lagrangian approach and leads to an algorithm for the computation of the optimal control. The obtained results are illustrated by numerical simulations which lead to some conjectures. 






NEW INEQUALITIES OF HERMITEHADAMARD AND FEJÉR TYPE VIA PREINVEXITY


Muhammad Amer Latif,


Abstract
: 

Several new weighted inequalities connected with HermiteHadamard and Fejér type inequalities are established for functions whose derivatives in
absolute value are preinvex. The results presented in this paper provide extensions of those given in earlier works. 






Numerical solution of model of cancer invasion with tissue


Mohammad Bagher Ghaemi,


Abstract
: 

Chemotaxishaptotaxis model of cancer invasion with tissue remodeling is one of the important PDE’s system in medicine, mathematics and biomathematics. In this paper we find the solution of chemotaxishaptotaxis model of cancer invasion using the new homotopy perturbation method (NHPM). Then by comparing some estimated numerical result with simulation laboratory result, its shown that NHPM is an efficient and exact way for solving cancer PDE’s
system. 






Mathematical analysis of virus dynamics model with multitarget cells in vivo


Ahmed Bakr,


Abstract
: 

This paper investigates the qualitative behavior of viral infection model with multiple delays in vivo. The infection rate is given by CrowleyMartin functional response. By assuming that the virus
attack $n$ classes of uninfected target cells, we study a viral infection model of dimension $2n+1$ with discrete delay. To describe the latent period for the contacted target cells with viruses to begin producing viruses, two types of discrete delay are incorporated into the model. The basic reproduction number $R_{0}$
of the model is defined which determines the dynamical behaviors of the model. Utilizing Lyapunov functionals and LaSalles invariance principle, we have proven that if $R_{0}\le{1}$ then the uninfected steady state is globally asymptotically stable, and if $R_{0}>1$
then the infected steady state is globally asymptotically stable. 






Some Modifications of Adomian’s Decomposition Method for Fractional Partial Differential Equations


Jamshad Ahmad,


Abstract
: 

In this paper, we present some modifications of Adomian’s Decomposition Method (ADM) to obtain analytical exact and approximate solutions for initial value problems of fractional order. The fractional derivative is defined in the Jumarie’s sense. The results are compared with those obtained using the Fractional Adomian’s Decomposition Method (ADM). The effectiveness and good accuracy of each modified is verified by the numerical results. 






Some integral inequalities in terms of supremum norms of $n$time differentiable functions


ShuHong Wang,
BoYan Xi,
Feng Qi,


Abstract
: 

In the paper, the authors establish identities for $n$time differentiable functions and obtain some integral inequalities in terms of supremum norms of $n$time differentiable functions. These results generalize Ostrowskis and Simpsons inequalities. 






Higher order schemes for Solving Optimal Control Problems


Mostafs. A. ElKhateb,


Abstract
: 

We shall present a numerical procedure for solving optimal control problems with the extendedone step method. A control system is considered, and a cost functional is minimized. A class of optimal control problems governed by ordinary differential equations is presented. The control variables are approximated by a polynomial function and the state variables are obtained by solving a system of ordinary differential equations using extended onestep methods of order five and six. These methods are A and Lstable methods. The problem is reduced to either a constrained or unconstrained optimization problem according to the nature of the dynamic system and the given conditions, which can be solved using Hybrid penalty partial quadratic interpolation technique. 






Solving a class of nonlinear twodimensional Volterra integral equations by twodimensional triangular orthogonal functions


Farshid Mirzaee,


Abstract
: 

Twodimensional triangular orthogonal functions (2DTFs) are applied to solving a class of nonlinear twodimensional Volterra integral equations. Using 2DTFs, nonlinear twodimensional Volterra integral equations reduce to algebraic equations. The comparison of the results with the other numerical methods shows the efficiency and accuracy of this method. 






Global Nonexistence of Solutions for Systems of Quasilinear Hyperbolic Equations with Damping and Source Terms


Yaojun YE,


Abstract
: 

The initialboundary value problem for a class of quasilinear hyperbolic equations system in bounded domain is studied. We prove that the solutions with the positive initial energy blow up in finite time under some conditions. The estimates of the lifespan of solutions are given. 






Numerical approximation solutions for spacesymmetric fractional diffusion equation with variable stepsize in Riesz spaces


Youwei Zhang,


Abstract
: 

This paper presents numerical solution of Riesz fractional diffusion equation and Riesz fractional advectiondispersion equation on a bounded domain, our main concern is to obtain a general numerical
approximation schemes to solve these equations by introducing a variable space stepsize numerical approximation schemes. Two numerical methods are provided to deal with numerical solution of the Riesz space fractional derivatives, and an example are included to illustrate the results obtained. 






Bernoulli Matrix Approach for Solving Two Dimensional Linear Hyperbolic Partial Differential Equations with Constant Coefficients


EMRAN TOHIDI,


Abstract
: 

The purpose of this study is to give a Bernoulli polynomial approximation for the solution of hyperbolic partial differential equations with three variables and constant coefficients. For this purpose, a Bernoulli matrix approach is introduced. This method is based on taking the truncated Bernoulli expansions of the functions in the partial differential equations. After replacing the approximations of functions in the basic equation, we deal with a linear algebraic equation. Hence, the result matrix equation can be solved and the unknown Bernoulli coefficients can be found approximately. The efficiency of the proposed approach is demonstrated with one example. 






Unsteady Simulation of RotorStator Interaction in Axial Flow Pump Based on Computational Fluid Dynamics


Zhang Hua,
Shi Weidong,
Li Tongtong,
Yao Jie,


Abstract
: 

Investigations of the RotorStator Interaction in a axialflow pump at different conditions are presented in the paper. The numerical simulation of the unsteady flow field is performed with FLUENT codes based on RNG kε model and SIMPLEC arithmetic. Numerical results show that the strongcoupling evolutions of static pressure and axial velocity distribution between rotor and stator in multiconditions are periodic with the rotation of rotor. The interaction of stationary and rotating pressure field leads to periodic flow field distortions and induces pressure fluctuation. It is found that the maximum pressure amplitude of blade passing frequency occurs in the rotor inlet zone, but it deceases very fast backward to the stator. The dominant frequency at monitoring points located at rotor inlet, outlet and stator outlet, corresponds to the blade passage frequency. The axial velocity distortion resulting from the modulation of the interacting stationary and rotating flow field is affected by the blade numbers and thickness of both rotor and stator. The axial velocity shows different distributions at different conditions, and the phase of it changes cyclically. 






T, Sintuitionistic Fuzzy Finite State Machines


Masumeh Sadeghi,
Hamid AlinejadRokny,


Abstract
: 

The aim of this paper is the study of the notions of covering and direct product in TSintuitionistic fuzzy finite state machines. In this regards various kinds of products in such machines are defined and aim of algebraic properties of them are investigated. 






Anomaly intrusion Detection Based on PLS Feature Extraction and Core Vector Machine


Gan Xusheng et al,
Gan Xusheng et al,


Abstract
: 

To improve the ability of detecting anomaly intrusions, a combined algorithm is proposed based on Partial Least Square (PLS) feature extraction and Core Vector Machine (CVM) algorithms. Principal elements are firstly extracted from the data set using the feature extraction of PLS algorithm to construct the feature set, and then the anomaly intrusion detection model for the feature set is established by virtue of the speediness superiority of CVM algorithm in processing largescale sample data. Finally, anomaly intrusion actions are checked and judged using this model. Experiments based on KDD99 data set verify the feasibility and validity of the combined algorithm. 






Closed form solution of electromagnetic wave diffraction in a homogeneous biisotropic medium


Rab Nawaz,


Abstract
: 

We have presented a theoretical analysis of an electromagnetic scattering problem by a perfectly conducting strip surrounded by a homogeneous biisotropic medium. This study is focused on the exact and concise formulation for the acquisition of a closed form solution in complex domain. The complete solution of electromagnetic plane wave is presented by a series one whose eigenfunctions are the generalized Gamma functions occurring in the finite diffraction theory. The scattered field is discussed in physical domain by obtaining the convergence history of the problem in transformed domain. This analysis provides the higher order accuracy solution in closed form in physical domain. 






A novel proof of Watsons contour integral representations


DongFang Liu,
XiangLi Wang,


Abstract
: 

In this paper we give a simple proof of Watsons contour integral representations for $_{r+1}\phi_{r}$ by applying Cauchys operators, and obtain an interesting formula of contour integral representation for $(q;q)^r_\infty$. 






The approximate solution of Fredholm integralequations by using Chebyshev polynomials


M.H.Saleh,


Abstract
: 

In this paper, a numerical solution for solving the Fredholm integral equations of the second kind is
considered. An application of Chebyshev polynomial method is applied to solve the Fredholm integral
equations. Numerical examples are presented to illustrate the efficiency and accuracy of the method. 






Exact solution for fractionalized Maxwell fluid using Fox Hfunction


Muhammad Jamil,


Abstract
: 

The unsteady flow of a viscoelastic fractionalized (this word is suitable when fractional derivative is used in constitutive or governing equations) Maxwell fluid model, between two infinite coaxial circular cylinders, is studied by means of the Laplace and finite Hankel transforms. The motion is produced by the inner cylinder that at the initial moment is subject to a torsional time dependent shear stress. The solutions that have been obtained, presented under series form in terms of Fox Hfunctions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for ordinary Maxwell and Newtonian fluids appear as special cases of the present results. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations. 






ANALYTICAL SOLUTION OF SPACETIMEFRACTIONAL DERIVATIVE OF HYDRODYNAMIC DISPERSION ADVECTION EQUATION


Abdon Atangana,


Abstract
: 

Fractional advectiondispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. A spacetime fractional advectiondispersion equation (FADE) is a generalization of the classical ADE in which the firstorder space derivative is replaced with Caputo or RiemannLiouville derivative of order 0 


