International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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Backward Bifurcation in Lassa Fever Model

Abdurrahman Abdulhamid , Kabiru Muhammad

Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria.

Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria.

ABSTRACT

A Mathematical Model for Lassa which incorporates quarantine and re-infection was developed for the control of Lassa fever epidemic. The basic reproduction number is calculated and it is shown that the model exhibits the phenomenon of backward bifurcation where a stable endemic equilibrium coexists with a stable disease-free equilibrium when the associated reproduction number is less than unity. This phenomenon has epidemiological implication which shows the classical requirement of the associated reproduction number to be less than unity does not guarantee control of the disease. Sensitivity and uncertainty analysis were carried out to access the importance of each parameter of the model.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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Integro-Differential Functional Operator Control Systems:A Spectral Approach

Gamal N. Elnagar

University of South Carolina

ABSTRACT

The spectral methods of G. N. Elnagar, which yield spectral convergence rate for the approximate solutions of Fredholm and Volterra-Hammerstein integral equations, is generalized in order to solve the larger class of integro-differential functional operator control systems with spectral accuracy. The proposed method is based on the idea of relating spectrally constructed grid points to the structure of projection operators which will be used to approximate the control vector and the associated state vector. These projection operators are spectrally constructed using Lagrange polynomials as trial functions. Due to its dynamic nature, the proposed method avoids many of the numerical difficulties typically encountered in solving standard integro-differential functional equation control systems. An illustrated example is included to confirm the efficiency and applicability of the proposed method.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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AN ANALYTIC SOLUTION OF SIMPLIFIED MATHEMATICAL MODEL OF EQUATION OF CONTINUITY (CONSERVATION OF FLOW EQUATION).

Abdurrahman Abdulhamid , Kabiru Muhammad , Zahraddeen Abdullahi

Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria.

Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria.

Department of Statistics, Kano State Polytechnic, P.M.B. 3401, Kano, Nigeria.

ABSTRACT

Abstract
An analytic method of solving a partial differential equation (PDE) obtained from a modeled equation of continuity (conservation of flow equation) using integral transform method was proposed. The analysis of the equation was carried out with regards to the distance along road (x), time (t) and traffic flow (k). Whereas density of traffic (k0) and velocity (u) values were varied to asses how the vehicular flux changes in the study, one after the other keeping the rest fixed in order. The solution of the problem was discussed after analyzing the effect of the parameters on the traffic flow and graphs were presented to illustrate the exactness of the analytical solution where the behaviour of the traffic flux changes with distance for different initial densities and changes with distance for different initial velocities.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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14

Effect of the same degenerate additive noise on a
coupled system of reaction-diffusion equations

Wael W. Mohammed

Department of Mathematics, Faculty of Science, Hail University, Saudi Arabia

ABSTRACT

In this paper we present a class of stochastic system of reaction-diffusion equations. Our aim of this paper is to approximate the solutions for the system via amplitude equation with Neumann boundary conditions. We are interested on a systems that have nonlinear polynomial and give applications as Lotka-Volterra system and from chemistry the Brusselator model for the Belousov-Zhabotinsky chemical reaction to illustrate our results.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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14

Diamond-Alpha Steffensen's Inequality on Time Scales

A. A. El-Deeb

Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.

ABSTRACT

In this paper, we prove some new Steffensen-type inequalities
on time scales via the diamond-alpha dynamic integral, which is
defined as a linear combination of the delta and nabla integrals. These
inequalities extend some known dynamic inequalities on time scales and also unify
some continuous inequalities and their corresponding discrete
analogues.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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A Comparison Study Between the Two Wiener-Ito Expansions
In Solving Stochastic Differential Equations

Maha Hamed , Ibrahim Al-Kalla , Mohamed El-Beltagy , Beih El-desouky

Department of Mathematics, Faculty of Science, Mansoura University,Mansoura. Egypt

Engineering Mathematics and Physics Dept, Faculty of Engineering, Mansoura University, Mansoura, Egypt.

Engineering Mathematics and Physics Dept, Faculty of Engineering, Cairo University,Giza, Egypt.

Department of Mathematics, Faculty of Science, Mansoura University,Mansoura. Egypt

ABSTRACT

In this paper, the two known Wiener-Ito expansions are compared. The methodology, performance and convergence of the two expansions are shown. The two expansions are used in solving linear and nonlinear stochastic differential equations (SDEs). The first expansion, known also as Wiener-Hermite Expansion (WHE), is truncated only in one parameter, order, but it is more difficult to handle. The second expansion, known also as Wiener-Chaos Expansion (WCE), is truncated in two parameters, order and dimension, but it is more easier. The two expansions are shown to be powerful tools when the Gaussian and/or non-Gaussian solutions are intended.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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On two general nonlocal problems of an arbitrary (fractional) orders differential equations

Sheren Ahmed , Fatma Gaafar

Lecturer

Assistant Professor

ABSTRACT

In this paper, we prove some local and global existence theorems for a fractional orders differential equations with nonlocal conditions, also the uniqueness of the solution will be studied.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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Approximate Controllability for the Parabolic Equations

REZZOUG Imad , AYADI Abdelhamid

OUM EL BOUAGHI UNIVERSITY. ALGERIA

OUM EL BOUAGHI UNIVERSITY. ALGERIA

ABSTRACT

In this intervention, we study an approximate controllability problem. This problem appears naturally of approximate sentinel. The main tool is a theorem of uniqueness of the solution of ill-posed Cauchy problem for the parabolic equations.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

9

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Exact solutions for coupled nonlinear partial differential equations using G'/G method

U.M. Abdelsalam

Department of Mathematics, Faculty of Science, Fayoum University, Egypt.

ABSTRACT

(G'/G)-expansion method is examined to solve the Boiti–Leon–Pempinelli (BLP) system
and the (2 + 1)-dimensional breaking soliton system. The results show that this method is a
powerful tool for solving systems of nonlinear PDEs., it presents exact travelling wave solutions. The obtained solutions include rational, periodical, singular, shock wave and solitary wave solutions.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

10

14

Analytical solutions of fractional Huxley equation
by residual power series method

Dr. Anas Arafa , Ghada Elmahdy

Department of Mathematics and Computer Science, Faculty of Science, Port Said University

Department of Mathematics and Computer Science, Faculty of Science, Port Said University

ABSTRACT

This paper investigates the approximate solution of nonlinear Huxley equation using
new analytic technique. The solution was calculated in the form of a convergent
power series with easily computable components. The proposed method obtains
Taylor expansion of the solution and reproduces the exact solution when the solution
is polynomial.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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An Inverse Problem for Delay Differential Equations in Biological Systems with Memory

Fathalla A. Rihan

Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE

ABSTRACT

In this talk, we present the theoretical framework to solve inverse problems for Delay Differential Equations (DDEs). Given a parameterized DDE and experimental data, we estimate the parameters appearing in the model, using least squares approach.
Some issues associated with the inverse problem, such as nonlinearity and discontinuities which make the problem more ill-posed, are studied.
Sensitivity and robustness of the models to small perturbations in the parameters, using variational approach, are also investigated. The sensitivity functions may provide guidance for the modelers to determine the most informative data for a specific parameter, and select the best fit model.
The consistency of delay differential equations with bacterial cell growth is shown by fitting the models to real observations.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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Oscillation Theorems for Nonlinear Differential Equations of Third-Order

M. M. A. El-Sheikh , R. Sallam , S. Salem

Menoufia University

Menoufia University

Menoufia University

ABSTRACT

The aim of this paper is to study the oscillatory behavior of solutions of the third order neutral differential equation
(a(t)[z′′(t)]^{γ})′+∑_{i=1}^{m}f_{i}(t,x(σ_{i}(t)))=0, t≥t₀,
where z(t)=x(t)+∑_{j=1}ⁿp_{j}(t)x(τ_{j}(t)), m,n are positive integers, γ≥1 is a ratio of two odd positive integers and τ_{i}(t)≤t for i=1,2,..,m. A new criteria guarantees that every solution is either oscillatory or tends to zero are established. The obtained results improve some known results in the literature. Some examples are given to illustrate our results.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

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Discrete spline Numerov method for solving Swift-Hohenberg equation

W. K. Zahra , S. M. Elkoly

Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt and Department of Mathematics, Basic and Applied Sciences School, Egypt-Japan University of Science and Technology, New Borg El-Arab City, Alexandria, 21934, Egypt

Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El Sheikh Univ., Egypt

ABSTRACT

Discrete spline function based method is developed to solve the time fractional Swift-Hohenberg equation in the sense of Riemann Liouville derivative. Via Fourier method, the developed method is convergent and unconditionally stable. Numerical results are demonstrated to confirm the applicability and the theoretical results.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Differential Equation and Applications.

14

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Gehring Dynamic Inequalities and Higher Integrability Theorems

Sami H. Saker

Prof. Math. Department of Mathematics, Faculty of Science, Mnsoura University, Egypt

ABSTRACT

In this talk I will present new dynamic inequalities based on the application of the time scale version of Hardy's type inequality on a finite interval [a,b]_{T} where T is a time scale. Next, we will speak about Gehring's type inequalities on time scales by employing the obtained inequality. As an application of Gehring inequalities, we will prove some interpolation. Next, we will prove a dynamic inequality of Shum's type on a time scale T. The proof is new and different from the proof due to Shum. [Canad. Math. Bull. 14 (1971), 225-230]. Next, we prove some new integrability theorems which as a special case, when T=R, contain the results due to Muckenhoupt [Tran. Amer. Math. Soc. 165 (1972), 207-226] and the results due to Bojarski, Sbordone and Wik. [Studia Mat. VII, 10 (1992), 155-163]. By employing theorems, we will prove a higher integrability result which proves that the space L_{Δ}^{q}(0,T]_{T} of nonincreasing functions will be in the space L_{Δ}^{p}(0,T]_{T} for p>q. The results contain, as a special case, the integrability results due to Alzer [J. Math. Anal. Appl. 190 (1995), 774-779]. When T=N our results are essentially new and can be applied on different types of time scales.
2010 Mathematics Subject Classification: 26D15, 34A40, 34N05, 39A12.