Publications Scientifiques
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Item 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 On approximate controllability of impulsive fractional semilinear systems with deviated argument in hilbert spaces(InforMath Publishing Group, 2020) Aimene, DjihadIn this paper we apply a fixed-point theorem to study the existence and uniqueness of a mild solution and the approximate controllability of a fractional order impulsive differential equation with deviated argument in Hilbert spaces. An example is provided to show the effectiveness of the theoryItem 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 spaces