Publications Scientifiques
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Item Controllability of nonlocal Hilfer fractional delay dynamic inclusions with non-instantaneous impulses and non-dense domain(Springer, 2022) Boudjerida, Assia; Seba, DjamilaThe 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 outcomesItem Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay(Elsevier, 2019) Aimene, Djihad; Baleanu, D.; Seba, DjamilaWe discuss the controllability of semilinear differential equations of fractional order with impulses and delay. We make use of the Atangana-Baleanu derivative. Our main tools are semigroup theory, the fixed point theorem due to Darbo and their combination with the properties of measures of noncompactness. Our abstract results are well supported by an illustrative example.Item Controllability of impulsive fractional functional evolution equations with infinite state-dependent delay in Banach spaces(Wiley, 2021) Aimene, Djihad; Seba, Djamila; Laoubi, KarimaMany evolutionary processes from various fields of physical and engineering sciences undergo abrupt changes of state at certain moments of time between intervals of continuous evolution. These processes are more suitably modeled by impulsive differential equations. In this paper, we study the controllability of an impulsive fractional differential equation with infinite state-dependent delay in an arbitrary Banach space. We apply semigroup theory and Schaefer fixed point theorem. As an application, we include an example to illustrate the theoryItem 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, KarimaIn 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 calculusItem Controllability for Semilinear Fractional Integro-differential Systems with Deviated Argument in Banach Spaces(IEEE, 2020) Aimene, Djihad; Seba, Djamila; Laoubi, KarimaIn this work we will rely on the technique application of semigroup theory and fixed point theorem “Banach contraction” to demonstrate that there exists a mild solution to this type of controllability for semilinear fractional integro-differential equations with deviated arguments in Banach spacesItem Controllability results of Fractional Non-instantaneous Impulsive Semilinear Differential Inclusions with Infinite delay(IEEE, 2020) Boudjerida, Assia; Seba, Djamila; Laoubi, KarimaIn 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