]>
2018
18
4
71
Exponential form for Lyapunov function and stability analysis of the fractional differential equations
Exponential form for Lyapunov function and stability analysis of the fractional differential equations
en
en
This paper deals with an exponential form for Lyapunov function, in perspective to analyze the Lyapunov characterization of the Mittag-Leffler stability and the asymptotic stability for the fractional differential equations. In addition, a new Lyapunov characterization of Mittag-Leffler stability for fractional differential equations will be introduced. The exponential form will be used to prove the Lyapunov characterization of several stability notions, used in fractional differential equations. In this paper, the Caputo fractional derivative operator will be used to do the studies.
388
397
Ndolane
Sene
Laboratoire Lmdan, Departement de Mathematiques de la Decision, Faculte des Sciences Economiques et Gestion
Universite Cheikh Anta Diop de Dakar
Senegal
ndolanesene@yahoo.fr
Caputo fractional derivative
fractional differential equations
asymptotic stability
Article.1.pdf
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]
Parameters identification and dual synchronization between different chaotic and hyperchaotic systems
Parameters identification and dual synchronization between different chaotic and hyperchaotic systems
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en
This paper investigates the adaptive dual synchronization of
completely different four chaotic and hyperchaotic systems with
unknown parameters. Based on the Lyapunov stability theory, an
efficient adaptive synchronization controller is constructed that
converges the synchronization error signals to the origin with
sufficient transient speed. Suitable adaptive laws of unknown
parameters are designed that converged the estimated values of the
unknown parameters to the true values of the systems parameters.
Two numerical examples are presented and simulation results are
derived to illustrate the effectiveness of the proposed dual
synchronization approach.
398
410
A. Othman
Almatroud
Mathematics Department, Faculty of Science
University of Hail
Kingdom of Saudi Arabia
othman_almatroud@yahoo.com
M. S. M.
Noorani
School of Mathematical Sciences
Universiti Kebangsaan Malaysia
Malaysia
msn@ukm.edu.my
M. Mossa
Al-sawalha
Mathematics Department, Faculty of Science
University of Hail
Kingdom of Saudi Arabia
sawalha_moh@yahoo.com
Chaos
dual synchronization
adaptive control
unknown parameters
Lyapunov stability theory
Article.2.pdf
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]
Inherent irreversibility analysis in a buoyancy induced magnetohydrodynamic couple stress fluid
Inherent irreversibility analysis in a buoyancy induced magnetohydrodynamic couple stress fluid
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en
This paper investigates the inherent irreversibility in a buoyancy induced magnetohydrodynamic (MHD) couple stress fluid through non-Darcian porous medium. It is assumed that the fluid exchanges heat with the ambient following Newtonian law. The governing Navier-Stoke and energy equations are formulated and non-dimensionalied, the approximate solutions for the velocity and temperature profiles are obtained via Adomian decomposition method. The results are used to calculate the entropy generation rate, and Bejan number. The effects of Buoyancy force, suction/injection, Hartman number and other flow parameters on velocity, temperature, entropy generation rate, and Bejan number are analyzed and discussed graphically. The results show that increase in Buoyancy force and suction/injection increases fluid velocity and temperature.Entropy generation rate becomes higher as the values of Buoyancy force, suction/injection parameter, and Hartman number increases.
411
422
Jacob A.
Gbadeyan
Department of Mathematics
Department of Mathematics
University of Ilorin
Covenant University
Nigeria
Nigeria
j.agbadeyan@yahoo.com
Abiodun A.
Opanuga
Department of Mathematics
Covenant University
Nigeria
abiodun.opanuga@covenantuniversity.edu.ng
Buoyancy force
MHD
porous medium
entropy generation
Adomian decomposition method
Article.3.pdf
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]
A reliable analytic study for higher-dimensional telegraph equation
A reliable analytic study for higher-dimensional telegraph equation
en
en
In this study, we propose a developed semi-analytic technique, so called the
generalized residual power series method, to process higher-dimensional
linear and nonlinear partial differential equations. The obtained solution
is expressed in a form of rapidly convergent power series with easily
computable coefficients. Solution can, in turn, be termed in an exact closed
form. The results indicate the reliability, efficiency, and simplicity of the
proposed scheme. This is achieved by handling the \((m+1)\)-dimensional
hyperbolic telegraph equation.
423
429
Emad
Az-Zo'bi
Department of Mathematics and Statistics
Mutah University
Jordan
eaaz2006@yahoo.com
Generalized residual power series method
convergence analysis
exact solution
higher-dimensional partial differential equation
telegraph equation
Article.4.pdf
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Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART
Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART
en
en
We investigate a general HIV infection model with three types of infected
cells: latently infected cells, long-lived productively infected cells, and
short-lived productively infected cells. We consider two kinds of target
cells: CD4\(^{+}\) T cells and macrophages. We incorporate three discrete time
delays into the model. Moreover, we consider the effect of humoral immunity on
the dynamical behavior of the HIV. The HIV-target incidence rate,
production/proliferation, and removal rates of the cells and HIV are
represented by general nonlinear functions. We show that the solutions of the
proposed model are nonnegative and ultimately bounded. We derive two threshold
parameters which determine the stability of the three steady states of the
model. Using Lyapunov functionals, we established the global stability of the
steady states of the model. The theoretical results are confirmed by numerical simulations.
430
452
A. M.
Elaiw
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
a_m_elaiw@yahoo.com
E. Kh.
Elnahary
Department of Mathematics, Faculty of Science
Sohag University
Egypt
HIV infection
humoral immune response
latency
viral reservoirs
Article.5.pdf
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]
Second Hankel determinant for a class defined by modified Mittag-Leffler with generalized polylogarithm functions
Second Hankel determinant for a class defined by modified Mittag-Leffler with generalized polylogarithm functions
en
en
In this work, a new generalized derivative operator \( \mathfrak{M}_{\alpha,\beta,\lambda}^{m}\) is introduced. This operator obtained by using convolution (or Hadamard product) between the linear operator of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright \(_{p}\Psi_{q}\) function and generalized polylogarithm functions defined by
\[
\mathfrak{M}_{\alpha,\beta,\lambda}^{m}f(z)=\mathfrak{F}_{\alpha,\beta}f(z)*\mathfrak{D}_{\lambda}^{m}f(z)
= z+\sum_{n=2}^{\infty}\frac{\Gamma(\beta)n^{m}(n+\lambda-1)!}{\Gamma[\alpha(n-1)+\beta]\lambda ! (n-1)!}a_{n}z^{n},
\]
where \(m \in \mathbb{N}_{0} = \{0,1,2,3,\ldots\}\) and \(\min\{Re(\alpha),Re(\beta)\}>0\). By making use of \(\mathfrak{M}_{\alpha,\beta,\lambda}^{m}f(z)\), a class of analytic functions is introduced. The sharp upper bound for the nonlinear \(|a_{2}a_{4}-a_{3}^{2}|\) (also called the second Hankel functional) is obtained. Relevant connections of the results presented here with those given in earlier works are also indicated.
453
459
M. N. M.
Pauzi
School of Modelling and Data Science (Previously: School of Mathematical Sciences), Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
nazran@unisel.edu.my
M.
Darus
School of Modelling and Data Science (Previously: School of Mathematical Sciences), Faculty of Science and Technology
Universiti Kebangsaan Malaysia
Malaysia
maslina@ukm.edu.my
S.
Siregar
Department of Science and Biotechnology, Faculty of Engineering and Life Sciences
Universiti Selangor
Malaysia
saibah@unisel.edu.my
Hankel determinant
modified Mittag-Leffler function
polylogarithms functions
Article.6.pdf
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