


Paper's Title:
HyersUlamRassias Stability of a Generalized Jensen Functional Equation
Author(s):
A. Charifi, B. Bouikhalene, E. Elqorachi and A. Redouani
Department of
Mathematics, Faculty of Sciences,
Ibn Tofail University,
Kenitra, Morocco
charifi2000@yahoo.fr
bbouikhalene@yahoo.fr
Department of
Mathematics, Faculty of Sciences,
Ibn Zohr University,
Agadir, Morocco
elqorachi@hotmail.com
Redouaniahmed@yahoo.fr
Abstract:
In this paper we obtain the HyersUlamRassias stability for the generalized Jensen's functional equation in abelian group (G,+). Furthermore we discuss the case where G is amenable and we give a note on the HyersUlamstability of the Kspherical (n × n)matrix functional equation.
Paper's Title:
On Ruled Surfaces According to QuasiFrame in Euclidean 3Space
Author(s):
M. Khalifa Saad and R. A. AbdelBaky
Department of Mathematics, Faculty of
Science,
Islamic University of Madinah,
KSA.
Department of Mathematics, Faculty of Science,
Sohag University, Sohag,
EGYPT.
Email:
mohamed_khalifa77@science.sohag.edu.eg,
mohammed.khalifa@iu.edu.sa
Department of Mathematics, Faculty of
Science,
Assiut University, Assiut,
EGYPT.
Email: rbaky@live.com
Abstract:
This paper aims to study the skew ruled surfaces by using the quasiframe of Smarandache curves in the Euclidean 3space. Also, we reveal the relationship between SerretFrenet and quasiframes and give a parametric representation of a directional ruled surface using the quasiframe. Besides, some comparative examples are given and plotted which support our method and main results.
Paper's Title:
Ulam Stability of Reciprocal Difference and Adjoint Functional Equations
Author(s):
K. Ravi, J. M. Rassias and B. V. Senthil Kumar
Department of Mathematics,
Sacred Heart College, Tirupattur  635601,
India
Pedagogical Department E. E.,
Section of Mathematics and Informatics,
National and Capodistrian University of Athens,
4, Agamemnonos Str., Aghia Paraskevi,
Athens, Attikis 15342,
GREECE
Department of Mathematics,
C.Abdul Hakeem College of Engineering and
Technology, Melvisharam  632 509, India
shckavi@yahoo.co.in
jrassias@primedu.uoa.gr
bvssree@yahoo.co.in
Abstract:
In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or UlamGavrutaRassias) stability problem for the same equations.
Paper's Title:
Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and realvalued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.
Paper's Title:
Solving NonAutonomous Nonlinear Systems of Ordinary Differential Equations Using MultiStage Differential Transform Method
Author(s):
K. A. Ahmad, Z. Zainuddin, F. A. Abdullah
School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM Penang
Malaysia.
Email: abumohmmadkh@hotmail.com
zarita@usm.my
farahaini@usm.my
Abstract:
Differential equations are basic tools to describe a wide variety of phenomena in nature such as, electrostatics, physics, chemistry, economics, etc. In this paper, a technique is developed to solve nonlinear and linear systems of ordinary differential equations based on the standard Differential Transform Method (DTM) and Multistage Differential Transform Method (MsDTM). Comparative numerical results that we are obtained by MsDTM and RungeKutta method are proposed. The numerical results showed that the MsDTM gives more accurate approximation as compared to the RungeKutta numerical method for the solutions of nonlinear and linear systems of ordinary differential equations
Paper's Title:
Weak Solution for Hyperbolic Equations with a NonLocal Condition
Author(s):
Lazhar Bougoffa
King Khalid
University, Faculty of Science, Department of Mathematics,
P.O.Box 9004, Abha, Saudi Arabia
abogafah@kku.edu.sa
Abstract:
In this paper, we study hyperbolic equations with a nonlocal condition. We prove the existence and uniqueness of weak solutions, using energy inequality and the density of the range of the operator generated by the problem.
Paper's Title:
Kinematic Model for Magnetic Nullpoints in 2 Dimensions
Author(s):
Ali Khalaf Hussain AlHachami
Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
Email: alhachamia@uowasit.edu.iq
Abstract:
The adjacent configurations of twodimensional magnetic null point centers are analyzed by an immediate examination about the null. The configurations are classified as either potential or nonpotential. By then the nonpotential cases are subdivided into three cases depending upon whether the component of current is less than, equal to or greater than a threshold current. In addition the essential structure of reconnection in 2D is examined. It unfolds that the manner by which the magnetic flux is rebuilt. In this paper, we center on the ramifications of kinematic arrangements; that is, we fathom just Maxwell's conditions and a resistive Ohm's law.
Paper's Title:
Generalised Models for Torsional Spine Reconnection
Author(s):
Ali Khalaf Hussain AlHachami
Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
Email: alhachamia@uowasit.edu.iq
Abstract:
Threedimensional (3D) null points are available in wealth in the solar corona, and the equivalent is probably going to be valid in other astrophysical situations. Ongoing outcomes from sun oriented perceptions and from reproductions propose that reconnection at such 3D nulls may assume a significant job in the coronal dynamics. The properties of the torsional spine method of magnetic reconnection at 3D nulls are researched. Kinematic model are created, which incorporate the term ηJ that is spatially localised around the null, stretching out along the spine of the null. The null point is to research the impact of shifting the level of asymmetry of the null point magnetic field on the subsequent reconnection process where past examinations constantly considered a nonnonexclusive radially symmetric null. Specifically we analyse the rate of reconnection of magnetic flux at the spine of null point. Logical arrangements are determined for the enduring kinematic equation, and contrasted and the after effects of torsional spine reconnection models when the current is restricted in which the Maxwell conditions are illuminated. The geometry of the current layers inside which torsional spine reconnection happen is autonomous on the symmetry of the magnetic field. Torsional spine reconnection happens in a thin cylinder around the spine, with circular crosssegment when the fan eigenvalues are extraordinary. The short axis of the circle being along the solid field bearing. Just as it was discovered that the fundamental structure of the method of attractive reconnection considered is unaffected by changing the magnetic field symmetry, that is, the plasma flow is discovered rotational around the spine of null point. The spatiotemporal pinnacle current, and the pinnacle reconnection rate achieved, are found not to rely upon the level of asymmetry.
Paper's Title:
Fractional exp(φ(ξ)) Expansion Method and its Application to SpaceTime Nonlinear Fractional Equations
Author(s):
A. A. Moussa and L. A. Alhakim
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Alaamath81@gmail.com
URL:
https://scholar.google.com/citations?user=ccztZdsAAAAJ&hl=ar
Department of Management Information
System and Production Management,
College of Business and Economics, Qassim University,
P.O. BOX 6666, Buraidah: 51452,
Saudi Arabia.
Email: Lama2736@gmail.com
URL:
https://scholar.google.com/citations?user=OSiSh1AAAAAJ&hl=ar
Abstract:
In this paper, we mainly suggest a new method that depends on the fractional derivative proposed by Katugampola for solving nonlinear fractional partial differential equations. Using this method, we obtained numerous useful and surprising solutions for the spacetime fractional nonlinear WhithamBroerKaup equations and spacetime fractional generalized nonlinear HirotaSatsuma coupled KdV equations. The solutions obtained varied between hyperbolic, trigonometric, and rational functions, and we hope those interested in the reallife applications of the previous two equations will find this approach useful.
Paper's Title:
New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces
Author(s):
S. S. Dragomir
School of Computer Science and Mathematics, Victoria
University of Technology, PO BOX
14428, MCMC 8001, VICTORIA, AUSTRALIA.
sever.dragomir@vu.edu.au
URL:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Abstract:
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.
Paper's Title:
Generalized FugledePutnam Theorem and Orthogonality
Author(s):
A. Bachir and A. Sagres
Department of
Mathematics, Faculty of Science, King Khaled
University, Abha, P.O. Box 9004 Kingdom Saudi Arabia
bachir_ahmed@hotmail.com
sagres@hotmail.com
Abstract:
An asymmetric FugledePutnam’s theorem for dominant operators and phyponormal operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.
Paper's Title:
Reverses of the Triangle Inequality in Inner Product Spaces
Author(s):
Sever S. Dragomir
School of Computer Science and Mathematics,
Victoria University Of Technology,
PO Box 14428, Mcmc 8001,
Victoria, Australia.
sever@csm.vu.edu.au
Url:
http://rgmia.vu.edu.au/SSDragomirWeb.html
Abstract:
Some new reverses for the generalised triangle inequality in inner product spaces are given. Applications in connection to the Schwarz inequality and for vectorvalued integrals are provided as well.
Paper's Title:
Boundary Value Problems for Fractional DiffusionWave equation
Author(s):
Varsha DaftardarGejji and Hossein Jafari
Department of Mathematics, University of Pune,
Ganeshkhind, Pune  411007,
INDIA.
vsgejji@math.unipune.ernet.in
jafari_h@math.com
Abstract:
Non homogeneous fractional diffusionwave equation has been solved under linear/nonlinear boundary conditions. As the order of time derivative changes from
0 to 2, the process changes from slow diffusion to classical diffusion to mixed diffusionwave behaviour.
Numerical examples presented here confirm this inference. Orthogonality of eigenfunctions in case of fractional StürmLiouville problem has been established
Paper's Title:
A Reverse of the Triangle Inequality in Inner Product Spaces and Applications for Polynomials
Author(s):
I. Brnetić, S. S. Dragomir, R. Hoxha and J. Pečarić
Department of Applied Mathematics, Faculty of Electrical
Engineering and Computing,
University of Zagreb, Unska 3, 10 000 Zagreb,
Croatia
andrea@zpm.fer.hr
School of Computer Science & Mathematics, Victoria University
Po Box 14428, Melbourne Vic 8001
Australia
sever.dragomir@vu.edu.au
URL:http://rgmia.vu.edu.au/dragomir
Faculty of Applied Technical Sciences, University of Prishtina,
Mother
Theresa 5, 38 000 Prishtina
Kosova
razimhoxha@yahoo.com
Faculty of Textile Technology, University of Zagreb,
Pierottijeva 6, 10000
Zagreb,
Croatia
pecaric@hazu.hr
Abstract:
A reverse of the triangle inequality in inner product spaces related to the celebrated DiazMetcalf inequality with applications for complex polynomials is given.
Paper's Title:
On Vector Variational Inequality Problem in Terms of Bifunctions
Author(s):
C. S. Lalitha and Monika Mehta
Department of Mathematics, Rajdhani College,
University of Delhi, Raja Garden,
Delhi 110015, India
cslalitha@rediffmail.com
Department of Mathematics, Satyawati College,
University Of Delhi, Ashok Vihar,
PhaseIII, Delhi 110052, India
mridul_in@yahoo.com
Abstract:
In this paper, we consider a generalized vector variational inequality problem expressed in terms of a bifunction and establish existence theorems for this problem by using the concepts of cone convexity and cone strong quasiconvexity and employing the celebrated Fan's Lemma. We also give two types of gap functions for this problem.
Paper's Title:
Salageantype Harmonic Univalent Functions with Respect to Symmetric Points
Author(s):
R. A. AlKhal and H. A. AlKharsani
Department of Mathematics, Faculty of Science, Girls College,
P.O. Box 838,
Dammam, Saudi Arabia
ranaab@hotmail.com
hakh@hotmail.com
Abstract:
A necessary and sufficient coefficient are given for functions in a class of complexvalued harmonic univalent functions of the form f=h+\g using Salagean operator where h and g are analytic in the unit disk U = {z:z<1}. Furthermore, distortion theorems, extreme points, convolution condition, and convex combinations for this family of harmonic functions are obtained.
Paper's Title:
ANormal Operators In Semi Hilbertian Spaces
Author(s):
A. Saddi
Department of Mathematics,
College of Education for Girls in Sarat Ebeidah 61914, Abha,
King Khalid University
Saudi Arabia
adel.saddi@fsg.rnu.tn
Abstract:
In this paper we study some properties and inequalities of Anormal operators in semiHilbertian spaces by employing some known results for vectors in inner product spaces. We generalize also most of the inequalities of (α,β)normal operators discussed in Hilbert spaces [7].
Paper's Title:
Existence and Regularity of Minima of an Integral Functional in Unbounded Domain
Author(s):
L. Aharouch, J. Bennouna and A. Bouajaja
King Khalid University
Faculty of Arts and Science Mha'l Asir
Saudi Arabia.
Email: laharouch@gmail.com
Université Sidi Mohammed Ben Abdellah
Faculté des Sciences DharMahraz
B.P 1796 Atlas Fès,
Maroc.
Email: jbennouna@hotmail.com
Email: kadabouajaja@hotmail.com
Abstract:
We prove the existence and the regularity of minima for a functional defined on a suitable Sobolev space.
Paper's Title:
Inequalities for Discrete FDivergence Measures: A Survey of Recent Results
Author(s):
Sever S. Dragomir^{1,2}
^{1}Mathematics, School of Engineering
& Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
Email: sever.dragomir@vu.edu.au
^{2}DSTNRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL:
http://rgmia.org/dragomir
Abstract:
In this paper we survey some recent results obtained by the author in providing various bounds for the celebrated fdivergence measure for various classes of functions f. Several techniques including inequalities of Jensen and Slater types for convex functions are employed. Bounds in terms of KullbackLeibler Distance, Hellinger Discrimination and Varation distance are provided. Approximations of the fdivergence measure by the use of the celebrated Ostrowski and Trapezoid inequalities are obtained. More accurate approximation formulae that make use of Taylor's expansion with integral remainder are also surveyed. A comprehensive list of recent papers by several authors related this important concept in information theory is also included as an appendix to the main text.
Paper's Title:
Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators
Author(s):
B. Deruni^{1}, A. S. Hacinliyan^{1,2}, E. Kandiran^{3}, A. C. Keles^{2}, S. Kaouache^{4}, M.S. Abdelouahab^{4}, N.E. Hamri^{4}
^{1}Department
of Physics,
University of Yeditepe,
Turkey.
^{2}Department
of Information Systems and Technologies,
University of Yeditepe,
Turkey
^{3}Department
of Software Development,
University of Yeditepe,
Turkey.
^{4}Laboratory
of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.
Email:
berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centrunivmila.dz
medsalah3@yahoo.fr
n.hamri@centreunivmila.dz
Abstract:
In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.
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