]>
2019
4
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58
Dynamics and stability results for impulsive type integro-differential equations with generalized fractional derivative
Dynamics and stability results for impulsive type integro-differential equations with generalized fractional derivative
en
en
In this paper, we investigate the existence, uniqueness, and Ulam stability of solutions for impulsive type integro-differential equations with generalized fractional derivative. The arguments are based upon the Banach contraction principle and Schaefer's fixed point theorem.
\begin{keyword}Integro-differential equations \sep impulsive differential equations \sep generalized fractional derivative \sep existence \sep Ulam-Hyers stablity.
\MSC{26A33\sep 34D10\sep 45N05.}
1
12
D.
Vivek
Department of Mathematics
P.S.G. College of Arts and Science
India
peppyvivek@gmail.com
E. M.
Elsayed
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
emmelsayed@yahoo.com
K.
Kanagarajan
Department of Mathematics
Sri Ramakrishna Mission Vidyalaya College of Arts and Science
India
kanagarajank@gmail.com
Integro-differential equations
impulsive differential equations
generalized fractional derivative
existence
Ulam-Hyers stablity
Article.1.pdf
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]
The Ulam's types stability of non-linear Volterra integro-delay dynamic system with simple non-instantaneous impulses on time scales
The Ulam's types stability of non-linear Volterra integro-delay dynamic system with simple non-instantaneous impulses on time scales
en
en
This manuscript presents Hyers-Ulam stability and Hyers-Ulam-Rassias stability results of non-linear Volterra integro-delay dynamic system on time scales with non-instantaneous impulses. Picard fixed point theorem is used for obtaining existence and uniqueness of solutions. By means of abstract Gronwall lemma, Gronwall's inequality on time scales and applications of Gronwall's inequality on time scales, we establish Hyers-Ulam stability and Hyers-Ulam-Rassias stability results. There are some primary lemmas, inequalities and relevant assumptions that helps in our stability results.
13
25
Syed Omar
Shah
Department of Mathematics
University of Peshawar
omarshahstd@uop.edu.pk
Akbar
Zada
Department of Mathematics
University of Peshawar
Pakistan
akbarzada@uop.edu.pk
Cemil
Tunc
Department of Mathematics, Faculty of Sciences
Yuzuncu Yil University
Turkey
cemtunc@yahoo.com
Hyers-Ulam stability
time scale
impulses
delay dynamic equation
Gronwall's inequality
abstract Gronwall lemma
Banach fixed point theorem
Article.2.pdf
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S. O. Shah, A. Zada, Connections between Ulam--Hyers stability and uniform exponential stability of time varying linear dynamic systems over time scales, Sohag J. Math., 6 (2019), 1-4
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S. O. Shah, A. Zada, Hyers--Ulam stability of non--linear Volterra integro--delay dynamic system with fractional integrable impulses on time scales, IJMSI., (), -
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S. O. Shah, A. Zada, A. E. Hamza, Stability analysis of the first order non-linear impulsive time varying delay dynamic system on time scales, Qual. Theory Dyn. Syst., 2019 (2019), 1-16
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]
Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to travelling harmonic load
Damping influence on the critical velocity and response characteristics of structurally pre-stressed beam subjected to travelling harmonic load
en
en
In this present study, the response characteristics of a flexible member carrying harmonic moving load are investigated. The beam is assumed to be of uniform cross section and has simple support at both ends. The moving concentrated force is assumed to move with constant velocity type of motion. A versatile mathematical approximation technique often used in structural mechanics called assumed mode method is in first instance used to treat the fourth order partial differential equation governing the motion of the slender member to obtain a sequence of second order ordinary differential equations. Integral transform method is further used to treat this sequence of differential equations describing the motion of the beam-load system. Various results in plotted curves show that, the presence of the vital structural parameters such as the axial force \(N\), rotatory inertia correction factor \(r^0\), the foundation modulus \(F_0\), and the shear modulus \(G_0\) significantly enhances the stability of the beam when under the action of moving load. Dynamic effects of these parameters on the critical speed of the dynamical system are carefully studied. It is found that as the values of these parameters increase, the critical speed also increase. Thereby reducing the risk of resonance and thus the safety of the occupant of this structural member is guaranteed.
26
36
B.
Omolofe
Department of Mathematical Sciences, School of Sciences
Federal University of Technology
Nigeria
babatope_omolofe@yahoo.com
T. O.
Adeloye
Department of Mathematics, Faculty of Basic Sciences
Nigeria Maritime University
Nigeria
adeyel@yahoo.com
Response characteristics
flexural member
harmonic load
critical speed
resonance
foundation stiffness
assumed mode
concentrated force
Article.3.pdf
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M. Abu-Hilal, H. Zibdeh, Vibration analysis of beams with general boundary conditions traversed by a moving force, J. Sound Vibratio, 229 (2000), 377-388
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]
A study on self-similar surfaces
A study on self-similar surfaces
en
en
In this paper, we study the self-similar surfaces in 4-dimensional Euclidean
space \(\mathbb{E}^{4}\). We give an if and only if condition for a generalized rotational surfaces in \( \mathbb{E}^4 \) to be self-similar. In addition we examine self-similarity of some special surfaces in \( \mathbb{E}^4 \). Furthermore we investigate the
self-similar condition of Tensor Product surfaces and Meridian surfaces in
\(\mathbb{E}^{4}\).
37
44
Mustafa
Altin
Bingol University
Vocational School of Technical Sciences
Turkey
maltin@bingol.edu.tr
Muge
Karadag
Inonu University
Faculty of Art and Science, Department of Mathematics
Turkey
muge.karadag@inonu.edu.tr
H. Bayram
Karadag
Inonu University
Faculty of Art and Science, Department of Mathematics
Turkey
bayram.karadag@inonu.edu.tr
Self similar surface
tensor product surfaces
generalized rotating surfaces
meridian surface
Article.4.pdf
[
]
Bernoulli polynomial and the numerical solution of high-order boundary value problems
Bernoulli polynomial and the numerical solution of high-order boundary value problems
en
en
In this work we present a fast and accurate numerical approach for
the higher-order boundary value problems via Bernoulli collocation
method. Properties of Bernoulli polynomial along with their
operational matrices are presented which is used to reduce the
problems to systems of either linear or
nonlinear algebraic equations. Error analysis is included.
Numerical examples illustrate the pertinent characteristic of the
method and its applications to a wide variety of model problems.
The results are compared to other methods.
45
59
Mohamed
El-Gamel
Department of Mathematics and Engineering Physics, Faculty of Engineering
Mansoura University
Egypt
gamel__eg@yahoo.com
Waleed
Adel
Department of Mathematics and Engineering Physics, Faculty of Engineering
Mansoura University
Egypt
waleedadel85@yahoo.com
M. S.
El-Azab
Department of Mathematics and Engineering Physics, Faculty of Engineering
Mansoura University
Egypt
ms__elazab@hotmail.com
Bernoulli
collocation
higher-order
astrophysics
error analysis
Article.5.pdf
[
]