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Fractional integro-differential inclusions with state-dependent delay

Khalida AissaniMouffak BenchohraKhalil Ezzinbi — 2014

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.

Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

Khalil EzzinbiGuy DeglaPatrice Ndambomve — 2015

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and...

Semilinear Functional Differential Equations of Fractional order with State-Dependent Delay

Mouffak BenchohraOmar BennihiKhalil Ezzinbi — 2013

Commentationes Mathematicae

In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon-Granas type for contractions maps in Frechet spaces combined with α -resolvent family is the main tool in our analysis.

Existence and controllability for nondensely defined partial neutral functional differential inclusions

Khalil EzzinbiSoumia Lalaoui Rhali — 2015

Applications of Mathematics

We give sufficient conditions for the existence of integral solutions for a class of neutral functional differential inclusions. The assumptions on the generator are reduced by considering nondensely defined Hille-Yosida operators. Existence and controllability results are established by combining the theory of addmissible multivalued contractions and Frigon's fixed point theorem. These results are applied to a neutral partial differential inclusion with diffusion.

Nonautonomous partial functional differential equations; existence and regularity

Moussa El-Khalil KpoumièKhalil EzzinbiDavid Békollè — 2017

Nonautonomous Dynamical Systems

The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring the existence...

Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

Abdelkarim-Nidal AkdadKhalil EzzinbiLotti Souden — 2015

Nonautonomous Dynamical Systems

In this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.

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