Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 14 (2019), 173 -- 193

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STABILITY IN NONLINEAR NEUTRAL LEVIN-NOHEL INTEGRO-DYNAMIC EQUATIONS

Kamel Ali Khelil, Abdelouaheb Ardjouni and Ahcene Djoudi

Abstract. In this paper we use the Krasnoselskii-Burton's fixed point theorem to obtain asymptotic stability and stability results about the zero solution for the following nonlinear neutral Levin-Nohel integro-dynamic equation

xΔ (t)+∫tt-τ (t) a(t,s)g(x(s)) Δ s+c(t)xΔ̃ (t-τ (t)) = 0.
The results obtained here extend the work of Ali Khelil, Ardjouni and Djoudi [5].

2010 Mathematics Subject Classification: 34K20, 34K30, 34k40.
Keywords: Fixed points; neutral integro-dynamic equations; stability; time scale.

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Kamel Ali Khelil
High School of Management Sciences Annaba,
Bp 322 Boulevard 24 February 1956, Annaba, 23000, Algeria.
e-mail: k.alikhelil@yahoo.fr

Abdelouaheb Ardjouni
Department of Mathematics and Informatics, University of Souk Ahras,
P.O. Box 1553, Souk Ahras, 41000, Algeria.
e-mail: abd_ardjouni@yahoo.fr

Ahcene Djoudi
Applied Mathematics Lab, Department of Mathematics, University of Annaba,
P.O. Box 12, Annaba 23000, Algeria.
e-mail: adjoudi@yahoo.com

http://www.utgjiu.ro/math/sma