$On a discretization process of fractional-order Logistic differential equation$

On a discretization process of fractional-order Logistic differential equation

In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant argument...

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Main Authors:	Z.F. El Raheem, S.M. Salman
Format:	Article
Language:	English
Published:	SpringerOpen 2014-10-01
Series:	Journal of the Egyptian Mathematical Society
Subjects:	Logistic differential equation Piecewise constant arguments Fractional-order differential equations Fixed points Lyapunov exponent Bifurcation
Online Access:	http://www.sciencedirect.com/science/article/pii/S1110256X13001235

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spelling	doaj-ada4ebc6170c42f78339aea60afaeb8e2020-11-25T01:22:13ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2014-10-0122340741210.1016/j.joems.2013.09.001On a discretization process of fractional-order Logistic differential equationZ.F. El RaheemS.M. SalmanIn this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.http://www.sciencedirect.com/science/article/pii/S1110256X13001235Logistic differential equationPiecewise constant argumentsFractional-order differential equationsFixed pointsLyapunov exponentBifurcation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Z.F. El Raheem S.M. Salman
spellingShingle	Z.F. El Raheem S.M. Salman On a discretization process of fractional-order Logistic differential equation Journal of the Egyptian Mathematical Society Logistic differential equation Piecewise constant arguments Fractional-order differential equations Fixed points Lyapunov exponent Bifurcation
author_facet	Z.F. El Raheem S.M. Salman
author_sort	Z.F. El Raheem
title	On a discretization process of fractional-order Logistic differential equation
title_short	On a discretization process of fractional-order Logistic differential equation
title_full	On a discretization process of fractional-order Logistic differential equation
title_fullStr	On a discretization process of fractional-order Logistic differential equation
title_full_unstemmed	On a discretization process of fractional-order Logistic differential equation
title_sort	on a discretization process of fractional-order logistic differential equation
publisher	SpringerOpen
series	Journal of the Egyptian Mathematical Society
issn	1110-256X
publishDate	2014-10-01
description	In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.
topic	Logistic differential equation Piecewise constant arguments Fractional-order differential equations Fixed points Lyapunov exponent Bifurcation
url	http://www.sciencedirect.com/science/article/pii/S1110256X13001235
work_keys_str_mv	AT zfelraheem onadiscretizationprocessoffractionalorderlogisticdifferentialequation AT smsalman onadiscretizationprocessoffractionalorderlogisticdifferentialequation
_version_	1725127042499870720

On a discretization process of fractional-order Logistic differential equation

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