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2018
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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
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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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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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]