]>
2019
4
1
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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]
Daftar-Gejii-Jafaris method for linear and nonlinear third order fractional differential equation
Daftar-Gejii-Jafaris method for linear and nonlinear third order fractional differential equation
en
en
Numerical solution of the third order fractional
differential equation is obtained by using DGJ (Daftardar-Gejii-Jafaris)
method. Providing DGJ method converges, it is shown that obtained
approximate solution is effective which is close to the exact solution or
the exact solution. An example explained this method is presented. The
proposed method is implemented for the approximation solution of the third
order nonlinear fractional partial differential equations. An example which
shows the method is unsuitable and inconsistent is given.
26
36
Mahmut
Modanli
Department of Mathematics, Faculty of Art and Science
Harran University
Turkey
mmodanli@harran.edu.tr
DGJ method
third order fractional differential equation
nonlinear differential equation
convergence
numerical solution
Article.3.pdf
[
]
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
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]
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
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