International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications. .::. Invited Lecture
1
SUN: 27-12-2015 Main Hall Invited Speaker Sec03 ( 1 )  
12:15 : 12:45
 
DEA - 15 GR Prof. I.P. STAVROULAKIS ipstav@uoi.gr
 
18
  OSCILLATIONS OF DELAY AND DIFFERENCE EQUATIONS WITH SEVERAL DEVIATING ARGUMENTS  
  I.P. STAVROULAKIS  
 
Department of Mathematics, University of Ioannina 451 10 Ioannina, Greece, Email: ipstav@uoi.gr
 
  ABSTRACT  
  -  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications. .::. Invited Lecture
2
MON: 28-12-2015 Main Hall Invited Speaker Sec08 ( 1 )  
11:00 : 11:30
 
DEA - 3 EG Prof. Samir Saker shsaker@mans.edu.eg
 
18
  Hardy and Opial Type Inequalities on time Scales  
  Samir H. Saker  
 
Department of Mathematics, Faculty of Science, Mansoura University, Egypt
 
  ABSTRACT  
  In the paper we present some new results related to Hardy and Opial type inequalities on time scales. The paper contains some of the recent published results.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
3
( )  
:
 
DEA - 16 NG Mr. OGUNTIFA OLUWAFEMI kazeemquadrioladapo@gmail.com
 
18
  Differential Equation and Applications.  
  Oguntifa Oluwafemi , AKANI GBENGA SAMUEL  
 
Mathimatices Equation
Application of Multiplication
 
  ABSTRACT  
   
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
4
( )  
:
 
DEA - 17 EG Dr. Enas soliman enasmohyi@yahoo.com
 
18
  Leibniz's rule and Fubini's theorem associated with a general quantum difference operator  
  Alaa E. Hamza , Enas M. Shehata  
 
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Department of Mathematics, Faculty of Science, Menoufia University, Egypt
 
  ABSTRACT  
  In this paper, we derive Leibniz's rule and Fubini's theorem associated with a general quantum difference operator $D_\beta$, which is defined by $D_\beta f(t)={(f(\beta(t))-f(t))}/{(\beta(t)-t)}$. Here $\beta$ is a strictly increasing continuous function defined on a set $I\subseteq\mathbb R$ that has only one fixed point $s_0\in I$.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
5
( )  
:
 
DEA - 18 EG Dr. Taher Bahnasy tbahnasy@ymail.com
 
18
  Solutions of Some Fractional Order Electrical Circuits Using Laplace Transform  
  W. K. Zahra , M. M. Hikal , Taher A. Bahnasy  
 
Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.
Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.
Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.
 
  ABSTRACT  
  In this paper, fractional linear electrical systems are investigated. Analytic solutions of the fractional models are derived using Laplace Transform method. Comparisons between fractional and classical electrical systems are illustrated using Laplace transform and Non-standard finite difference method.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
6
MON: 28-12-2015 Poster - Sec 01 ( 2 )  
11:30 : 12:15
 
DEA - 1 EG Dr. Mohamed Abdalla mabdomath85@gmail
 
18
  Some Integration Relations for Extension of Hypergeometric Matrix Functions of Two Complex Variables  
  M. Abdalla , A. K. Bakhet  
 
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
Department of Mathematics, Faculty of Science, Al-Azhar Assiut University, Assiut 71524, Egypt
 
  ABSTRACT  
  The main object of this paper is to present generalizations of hypergeometric matrix functions of two complex variables such as, Appell, Humbert and Horn matrix functions by means of the extended Beta matrix functions. A new integral representations are obtained for these new generalizations. Moreover, Hadamard product of the generalized Appell, Humbert and Horn matrix functions and some their integration properties are shown.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
7
MON: 28-12-2015 Poster - Sec 01 ( 2 )  
11:30 : 12:15
 
DEA - 8 EG Dr. Shoukry El-Ganaini ganaini5533@hotmail.com
 
18
  Solitons and other solutions to the (3+1)-dimensional quantum Zakharov-Kuznetsov (qZK)equation and its new extended form  
  Shoukry El-Ganaini  
 
Department of Mathematics, Faculty of Science, Damanhour University , Bahira 22514 , Egypt
 
  ABSTRACT  
  In this paper , the two variable (G/G,1/G) and (1/G)- expansion methods with the aid of Mathematica are used to construct exact traveling wave solutions with parameters of the (3+1)-dimensional quantum Zakharov-Kuznetsov (qZK)equation and its new extended form. When these parameters are taken particular values , the solitary wave solutions can be found to the considered equations . The obtained traveling wave solutions are expressed by the hyperbolic functions , the trigonometric functions and the rational functions. The used methods demonstrates power, reliability and efficiency and presents a wider applicability for handling nonlinear equations.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
8
MON: 28-12-2015 Poster - Sec 01 ( 2 )  
11:30 : 12:15
 
DEA - 6 EG Dr. Taher Bahnasy tbahnasy@ymail.com
 
18
  Solutions of Some Fractional Order Electrical Circuits Using Laplace Transform  
  W. K. Zahra , M. M. Hikal , Taher A. Bahnasy  
 
Egypt
Egypt
Egypt
 
  ABSTRACT  
  In this paper, fractional linear electrical systems are investigated. Analytic solutions of the fractional models are derived using Laplace Transform method. Comparisons between fractional and classical electrical systems are illustrated.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
9
MON: 28-12-2015 Poster - Sec 01 ( 2 )  
11:30 : 12:15
 
DEA - 10 EG Mr. Mostafa Khater mostafa.khater2024@yahoo.com
 
18
  Exact Traveling Wave Solutions for the generalized Hirota-Satsuma couple KdV system  
  Mostafa M. A. Khater  
 
Mansoura University
 
  ABSTRACT  
  In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota-Satsuma couple KdV system according to the exp(-φ(ξ))-expansion method and when these parameters are taken to be special values we can obtain the solitary wave solutions which is derived from the exact traveling wave solutions. It is shown that the proposed method provides a more powerful mathematical tool for constructing exact traveling wave solutions for many other nonlinear evolution equations.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
10
MON: 28-12-2015 Poster - Sec 01 ( 2 )  
11:30 : 12:15
 
DEA - 12 EG Ms. shaimaa salem shosho_ae2008@yahoo.com
 
18
  On the oscillatory behavior of third-order mixed neutral differential equations  
  M. M. A. El-Sheikh , R. Sallam , S. Salem  
 
Department of Mathematics, Faculty of Science, Menoufia University, Egypt
Department of Mathematics, Faculty of Science, Menoufia University, Egypt
Department of Mathematics, Faculty of Science, Menoufia University, Egypt
 
  ABSTRACT  
  The oscillation and nonoscillation of solutions of the nonlinear mixed neutral differential equation (a(t) (b(t) (x(t)+p_1 (t)x(τ_1 (t))+p_2 (t)x(τ_2 (t)))^' )^'β )^'+q(t)f(αx(t)+p_1 (t)x(σ_1 (t))+p_2 (t)x(σ_2 (t)))=0, where a(t),b(t),q(t) are positive functions, β>0 is the ratio of two odd positive integers and τ_1 (t),σ_1 (t)≤t,τ_2 (t),σ_2 (t)≥t is considered. New criteria are given using generalized Riccati trasformations. Illustrative examples are given to justify our results.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
11
MON: 28-12-2015 Poster - Sec 01 ( 2 )  
11:30 : 12:15
 
DEA - 13 EG Dr. Shoukry El-Ganaini ganaini5533@hotmail.com
 
18
  Exact solutions of an extended quantum Zakharov-Kuznetsov equation using the multiple simplest equation method  
  Shoukry El-Ganaini  
 
Department of Mathematics, Faculty of Science, Damanhour University , Bahira 22514 , Egypt
 
  ABSTRACT  
  The simplest equation method (SEM) presents a wide applicability for handling nonlinear evolution equations(NEEs) in mathematical physics .In this paper , a plethora of exact solutions are obtained to an extended quantum Zakharov-Kuznetsov equation via the applications of the simplest equation method (SEM) , modified simplest equation method (MSEM) and the extended simplest equation method (ESEM).The obtained solutions are in the form of hyperbolic , trigonometric and rational functions .The used methods are more effective and powerful than other approaches and can be applied to other nonlinear evolution equations(NEEs)in mathematical physics.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
12
MON: 28-12-2015 Poster - Sec 01 ( 2 )  
11:30 : 12:15
 
DEA - 14 EG Dr. Shoukry El-Ganaini ganaini5533@hotmail.com
 
18
  On the solutions and conservation laws of a nonlinear wave equation in semiconductors  
  Shoukry El-Ganaini  
 
Department of Mathematics, Faculty of Science, Damanhour University , Bahira 22514 , Egypt
 
  ABSTRACT  
  A nonlinear wave equation that arises in the study of semiconductors is studied. Exact traveling wave solutions are obtained using the two variable and - expansion methods.In addition , the conservation laws for the considered equation are also derived due to a new conservation theorem of Ibragimov.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
13
MON: 28-12-2015 Hall[C] Oral - Sec09 ( 1 )  
03:15 : 03:30
 
DEA - 2 EG Dr. Mohamed Elborhamy mmaelborhamy@yahoo.com
 
18
  Global Attractors For Systems of Integro-Differential Equations With Strongly Damped  
  Mohamed El-Borhamy  
 
Department of Engineering Physics and Mathematics- Faculty of Engineering - University of Tanta
 
  ABSTRACT  
  In this paper, we consider the long-time dynamical behavior of the following systems of integro-differential equations with strongly damped utt + Δu + ∫g1(t 􀀀 τ )Δu(τ )dτ -􀀀 Δut +􀀀 Δutt + ut = f1(u, v), vtt + Δv + ∫g2(t 􀀀 τ )Δv(τ )dτ 􀀀- Δvt +􀀀 Δvtt + vt = f2(u, v), u(x, 0) = u0(x), ut(x, 0) = u1(x), v(x, 0) = v0(x), vt(x, 0) = v1(x). and further prove the existence of global attractors for this system.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
14
MON: 28-12-2015 Hall[C] Oral - Sec09 ( 2 )  
03:30 : 03:45
 
DEA - 4 US Dr. Muhammad Hameed mhameed@uscupstate.edu
 
18
  Mathematical model to study neck elongation and pinch-off of a fluid thread  
  Muhammad Irfan Hameed  
 
Department of Mathematics, University of South Carolina, Spartanburg, USA
 
  ABSTRACT  
  Using slender-body theory, a mathematical model is developed to study the breakup of a fluid thread in viscous surrounding at low Reynold's number. We assume that a layer of insoluble surfactant is present at the interface. Equations governing the evolution of the interface and surfactant concentration are derived using long wavelength approximations. Numerical simulations of this long-wave asymptotic model show that the presence of surfactant at the interface retards the pinch-off and a slender quasi-steady thread is formed. After the formation of the thread, the diffusion of surfactant is found to play an important role and causes the jet to pinch. It is found that the presence of surfactant slows down the breakup process. Results of the long wavelength model are also compared against the numerical simulations of the full problem. The solution of the full problem shows similar behavior to the simplified model. It is found that the equation of state does not have much effect on the breakup.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
15
MON: 28-12-2015 Hall[C] Oral - Sec09 ( 3 )  
03:45 : 04:00
 
DEA - 5 CA Dr. Nasser Saad nsaad@upei.ca
 
18
  On the solvability of confluent Heun equation and associated orthogonal polynomials  
  Nasser Saad  
 
University of Prince Edward Island
 
  ABSTRACT  
  The present paper analyze the constraints on the confluent Heun type-equation, $(a_{3,1}r^2+a_{3,2}r)y''+(a_{2,0}r^2+a_{2,1}r+a_{2,2})y'-(\tau_{1,0}r+\tau_{1,1})y=0,$ where $|a_{3,1}|^2+|a_{3,2}|^2\neq 0, $ and $a_{i,j},i=3,2,1, j=0,1,2$ are real parameters, to admit polynomial solutions. The necessary and sufficient conditions for the existence of these polynomials are given. A three-term recurrence relation is provided to generate the polynomial solutions explicitly. We, then, prove that these polynomial solutions are a source of finite sequences of orthogonal polynomials. Several properties, such as the recurrence relation, Christoffel-Darboux formulas and the moments of the weight function, are discussed. We also show a factorization property of these orthogonal polynomials that allow for the construction of other sequences of orthogonal polynomials. For illustration, we examines the quasi- exactly solvability of the $(p,q)$-hyperbolic potential $V(r)=-V_0\sinh^p(r)/\cosh^q(r), V_0>0, p\geq 0, q>p$. The associated orthogonal polynomials generated by the solutions of the Schr\"odinger equation with the $(4,6)$-hyperbolic potential are constructed.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
16
MON: 28-12-2015 Hall[C] Oral - Sec09 ( 4 )  
04:00 : 04:15
 
DEA - 7 EG Mr. Amr AbdelAty a.m.abdelaty@fayoum.edu.eg
 
18
  Hermite Polynomials in the Fractional Order Domain  
  Amr M. AbdelAty , Ahmed Soltan , Waleed A. Ahmed , Ahmed G. Radwan  
 
Engineering Mathematics and Physics Dept, Faculty of Engineering, Fayoum University, Fayoum, Egypt.
School of Electrical, Electronic and Computer Engineering, Newcastle University, United Kingdom.
Engineering Mathematics and Physics Dept, Faculty of Engineering, Fayoum University, Fayoum, Egypt.
Engineering Mathematics and Physics Dept, Faculty of Engineering, Cairo University, Giza, 12613, Egypt. & Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza, Egypt.
 
  ABSTRACT  
  Due to the importance of its integer order counterpart in many mathematical and engineering fields, the fractional order Hermite polynomials are studied in this paper. A fractional variation of the well known Hermite differential equation is introduced based on Caputo fractional operator. The proposed equation is solved using fractional Taylor power series method and the convergence is verified using truncated series for different values of the parameters. The condition for fractional polynomial solution is obtained and the first four polynomials are scaled using an appropriate scaling factor. The fractional order Hermite filter based on these polynomials is introduced through its magnitude response as one possible application.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
17
MON: 28-12-2015 Hall[C] Oral - Sec09 ( 5 )  
04:15 : 04:30
 
DEA - 9 QA Prof. Mohamed Elgindi mohamed.elgindi@qatar.tamu.edu
 
18
  ON THE SOLVABILITY OF EULER GRAPHENE BEAM SUBJECT TO AXIAL COMPRESSIVE LOAD  
  Mohamad B. Elgindi , Dongming Wei , Tarek M. Elgindi  
 
Department of Mathematics, Faculty of Science, Texas A&M University at Qatar, Doha, Qatar
Department of Mathematics, School of Science and Technology, Nazarbayev Univesity, Astana, Kazakhstan
The Courant Institute, New-York University, New York, US
 
  ABSTRACT  
  In this paper we formulate the equilibrium equation for a beam made of graphene subjected to some boundary conditions and acted upon by axial compression and nonlinear lateral constrains as a fourth-order nonlinear boundary value problem. We first study the nonlinear eigenvalue problem for buckling analysis of the beam. We demonstrate the solvability of the eigenvalue problem as an asymptotic expansion in a ratio of the elastoplastic parameters. We verify that the spectrum is a closed set bounded away from zero and contains a discrete infinite sequence of eigenvalues. In particular, we prove the existence of a minimal eigenvalue for the graphene beam corresponding to a Lipschitz continuous eigenfunction, providing a lower bound for the critical buckling load of the graphene beam column. We also prove that the eigenfunction corresponding to the minimal eigenvalue is positive and symmetric. For a certain range of lateral forces, we demonstrate the solvability of the general nonlinear equation using energy methods and a suitable iteration scheme.  
 
 
International Conference for Mathematics
and Applications (ICMA15)
Academy of Scientific Research and Technology
27 – 29 DEC. 2015
Cairo, Egypt
 
 
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها 
أكاديمية البحث العلمي والتكنولوجيا
2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية
 
www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg
 

Differential Equation and Applications.
18
MON: 28-12-2015 Hall[C] Oral - Sec09 ( 6 )  
04:30 : 04:45
 
DEA - 11 EG Assoc.Prof. Abdallah A. Nahla a.nahla@science.tanta.edu.eg
 
18
  A Novel Fractional Technique for the Modified Point Kinetics Equations  
  Ahmed E. Aboanber , Abdallah A. Nahla  
 
Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt.
 
  ABSTRACT  
  The system of stiff coupled linear ordinary differential equations for the point kinetics equations (PKE) is one of the most important models in the nuclear science and engineering. This system describes the neutron density and the precursor concentrations of delayed neutrons in nuclear reactors. In the reactor dynamic systems, the relaxation time on the neutron density is one of the most important parameter arise from modified point kinetics equations (MPKE), which obtained from the non-Fickian effect of the space independent neutron diffusion equation. In this work, a fractional model for the modified point kinetics equations is derived and analyzed. An analytical method is used to solve the fractional model for the modified point kinetics equations. This methodical technique is based on the representation of the neutron density as a power series of the relaxation time as a small parameter. The validity of the fractional model is tested for different cases of step, ramp and sinusoidal reactivity. The results show that the fractional model for the modified point kinetics equations is the best representation of neutron density for supercritical reactors.