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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.3 Antofagasta Sept. 2016

http://dx.doi.org/10.4067/S0716-09172016000300004 

 

Asymptotic stability in delay nonlinear fractional differential equations

 

A. Ardjouni

Univ Souk Ahras, Algeria

H. Boulares 

University of Annaba, Algeria

A. Djoudi 

University of Annaba, Algeria


ABSTRACT

In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of delay nonlinear fractional differential equations of order . By using the Banach’s contraction mapping principle in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided that g (t, 0) = f (t, 0, 0) = 0, which include and improve some related results in the literature.

Subjclass [2000] : 34K20, 34K30, 34K40.

Keywords : Delay fractional differential equations, Fixed point theory, Asymptotic stability.


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 Received : November 2015. Accepted : June 2016

 

Abdelouaheb Ardjouni
Faculty of Sciences and Technology,
Department of Mathematics and Informatics,
 Univ Souk Ahras,

P. O. Box 1553,
Souk Ahras, 41000,
Algeria
e-mail: abd_ardjouni@yahoo.fr

Hamid Boulares
Depatement of Mathematics,
Faculty of Sciences,
University of Annaba,
P. O. Box 12,
Annaba, 23000,
Algeria
e-mail: boulareshamid@gmail.com

Ahcene Djoudi
Applied Mathematics Lab,
Faculty of Sciences, Department of Mathematics,
 University of Annaba,

P. O. Box 12,
Annaba 23000,
Algeria
e-mail: adjoudi@yahoo.com

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