Browsing by Author "Boudjerida, Assia"

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    Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses
    (Elsevier, 2021) Boudjerida, Assia; Seba, Djamila
    This paper deals with the approximate controllability of a class of non-instantaneous impulsive hybrid systems for fractional differential inclusions under Hilfer derivative of order 1<σ<2 and type 0≤ζ≤1, on weighted spaces. As an alternative to the Wright function which is defined only when 0<σ<1, we make use of a family of general fractional resolvent operators to give a proper form of the mild solution. This latter is consequently formulated by Laplace transform, improving and extending important results on this topic. Based on known facts about fractional calculus and set-valued maps, properties of the resolvent operator, and a hybrid fixed point theorem for three operators of Schaefer type, the existence result and the approximate controllability of our system is achieved. An example is given to demonstrate the effectiveness of our result
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    Controllability of coupled systems for impulsive φ- Hilfer fractional integro-differential inclusions
    (Taylor & Francis, 2020) Boudjerida, Assia; Seba, Djamila; N'Guérékata, G. M.
    This paper studies the controllability of a coupled system for a class of impulsive fractional integro-differential inclusions involving φ-Hilfer fractional derivative and subject to coupled nonlocal integral initial conditions in the case of convex set-valued maps. Some auxiliary conditions are introduced in order to apply a fixed point theorem due to Bohnenblust–Karlin. An illustrative example is provided to exemplify our theoretical results
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    Controllability of nonlocal Hilfer fractional delay dynamic inclusions with non-instantaneous impulses and non-dense domain
    (Springer, 2022) Boudjerida, Assia; Seba, Djamila
    The controllability of a class of nondensely defined fractional dynamic delay inclusions containing Hilfer fractional derivative, nonlocal conditions, and non-instantaneous impulses in abstract spaces is investigated without compactness assumption. The existence of an integral solution and the controllability for the given problem are established relying on a condensing fixed point theorem of multivalued maps. In support, an example is given to clarify the obtained theoretical outcomes
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    Controllability results for nondensely defined impulsive fractional-order functional semilinear differential inclusions in abstract space
    (American Institute of Physics, 2019) Boudjerida, Assia; Seba, Djamila; Laoubi, Karima
    In this work, we prove the controllability result of integral solutions defined on a real compact interval for a class of impulsive functional differential inclusions with fractional order and nonlocal conditions, in the case when the linear part is a non-densely defined operator and satisfies the Hille-Yosida condition. The main tool is an appropriate fixed point theorem, integrated semigroup, and the known facts about fractional calculus
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    Controllability results for some classes of fractional differential inclusions
    (Université M'hamad Bougara : Faculté des Sciences, 2021) Boudjerida, Assia; Seba, Djamila(Directeur de thèse)
    On s’intéresse dans cette thèse à la contrôlabilité de certains classes d’inclusions différentielles impulsives d’ordre fractionnaire avec retard, sous-différentiel de Clarke et des conditions non locales, sous trois types de dérivées fractionnaires (d’ordre 0 < < 1 et 1 < < 2). À cet effet, nous avons soumis un aperçu de l’analyse multivoques, et une brève étude sur certains faits liés au calcul fractionnel. De plus, nous avons présenté les techniques de base qui sont utilisées pour obtenir nos principaux résultats: mesure de non compacité, théorie des semi-groupes et le principe du point fixe. Ensuite, un nouvel ensemble des conditions suffisantes sont formulées afin d’assurer les résultats d’existence et les propriétés de la contrôlabilité et la contrôlabilité approchée pour les problèmes considérées. En outre, quelques exemples illustratifs sont assurés pour garantir l’efficacité de nos résultats théoriques obtenus
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    Controllability results of Fractional Non-instantaneous Impulsive Semilinear Differential Inclusions with Infinite delay
    (IEEE, 2020) Boudjerida, Assia; Seba, Djamila; Laoubi, Karima
    In the content of this paper, we will talk over the controllability results for an active type of impulsive fractional semilinear differential inclusions with non-instantaneous impulses and infinite delay by means of caputo fractional derivative. To establish our principal results we give some sufficient hypotheses, we use the Known facts about multivalued map and fractional calculus, and we employing the different techniques of fixed point theorem