Publications Scientifiques

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Author: search.filters.author.Seba, DjamilaHas files: No

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    Analysis of energy dissipation in hyperbolic problems influenced by internal and boundary control mechanisms
    (Taylor and Francis Ltd., 2024) Laoubi, Karima; Seba, Djamila
    This article primarily focuses on the rational stabilisation of the wave equation, supplied with a second-order dynamical boundary condition of hyperbolic type, while considering an additional internal damping mechanism within the specified ring. To achieve rational decay rates of the associated energy, it is imperative to exponentially stabilise a portion of the domain using a global Ingham's-type estimate. This paper will subsequently illustrate how this partially localised exponential stabilisation, combined with a Bessel analysis, leads to a rational decrease in the overall energy of the system considered.
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    Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition
    (Springer, 2024) Laoubi, Karima; Seba, Djamila
    This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family of eigenvalues of the corresponding operator, we prove that the rate of energy decay decreases in a polynomial way.
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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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    The WAF scheme for the isentropic drift-flux model of compressible two-phase flows
    (Elsevier, 2021) Ouffa, Souheyla; Zeidan, Dia; Seba, Djamila
    This paper focuses on the extension of the Weighted Average Flux (WAF) scheme for the numerical simulation of two-phase gas–liquid flow by imposing velocity equilibrium and without mechanical equilibrium of the transient drift-flux model. The model becomes a hyperbolic system of conservation laws with realistic closure relations where both phases are strongly coupled during their motion. Exploiting this, the drift-flux model discretization, simulation and investigation becomes very fast, simple and robust. The efficiency of the WAF scheme as being a second order in space and time without data reconstruction have been demonstrated in the published literature for compressible single-phase flows. However, the scheme is rarely applied to compressible two-phase flows. Based on a recent and complete exact Riemann solver for the drift-flux model, the model is numerically solved by the WAF scheme. The numerical algorithm accuracy and ability are validated through different published test cases. It is shown that the proposed scheme can be effectively employed to simulate two-phase flows involving discontinuities such as shocks and interfaces. The proposed WAF scheme is also compared with other numerical methods. Simulation results show appropriate agreement of WAF scheme even with the exact solutions. Comparisons of the presented simulations demonstrate that the behaviour of WAF scheme is encouraging, more accurate and fast than other numerical methods
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    The Henstock-Kurzweil-Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces
    (Wiley, 2021) Seba, Djamila; Habani, Sadek; Benaissa, Abbes; Rebai, Hamza
    This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multiorders fractional derivatives and deviating argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space. The applicability of the obtained results is illustrated by an example
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    Controllability of impulsive fractional functional evolution equations with infinite state-dependent delay in Banach spaces
    (Wiley, 2021) Aimene, Djihad; Seba, Djamila; Laoubi, Karima
    Many 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 theory
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    Controllability for Semilinear Fractional Integro-differential Systems with Deviated Argument in Banach Spaces
    (IEEE, 2020) Aimene, Djihad; Seba, Djamila; Laoubi, Karima
    In 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
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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
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    Reproducing kernel Hilbert space method for the numerical solutions of fractional cancer tumor models
    (2020) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader
    This research work is concerned with the new numerical solutions of some essential fractional cancer tumor models, which are investigated by using reproducing kernel Hilbert space method (RKHSM). The most valuable advantage of the RKHSM is its ease of use and its quick calculation to obtain the numerical solutions of the considered problem. We make use of the Caputo fractional derivative. Our main tools are reproducing kernel theory, some important Hilbert spaces, and a normal basis. We illustrate the high competency and capacity of the suggested approach through the convergence analysis. The computational results clearly show the superior performance of the RKHSM.
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    An efficient numerical technique for a biological population model of fractional order
    (ELSEVIER, 2021) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader
    In the present paper, a biological population model of fractional order (FBPM) with one carrying capacity has been examined with the help of reproducing kernel Hilbert space method (RKHSM). This important fractional model arises in many applications in computational biology. It is worth noting that, the considered FBPM is used to provide the changes that is made on the densities of the predator and prey populations by the fractional derivative. The technique employed to construct new numerical solutions for the FBPM which is considered of a system of two nonlinear fractional ordinary differential equations (FODEs). In the proposed investigation, the utilised fractional derivative is the Caputo derivative. The most valuable advantages of the RKHSM is that it is easily and fast implemented method. The solution methodology is based on the use of two important Hilbert spaces, as well as on the construction of a normal basis through the use of Gram-Schmidt orthogonalization process. We illustrate the high competency and capacity of the suggested approach through the convergence analysis. The computational results, which are compared with the homotopy perturbation Sumudu transform method (HPSTM), clearly show: On the one hand, the effect of the fractional derivative in the obtained outcomes, and on the other hand, the great agreement between the mentioned methods, also the superior performance of the RKHSM. The numerical computational are presented in illustrated graphically to show the variations of the predator and prey populations for various fractional order derivatives and with respect to time.