Publications Internationales
Permanent URI for this collectionhttps://dspace.univ-boumerdes.dz/handle/123456789/13
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Item Analysis of energy dissipation in hyperbolic problems influenced by internal and boundary control mechanisms(Taylor and Francis Ltd., 2024) Laoubi, Karima; Seba, DjamilaThis 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.Item Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition(Springer, 2024) Laoubi, Karima; Seba, DjamilaThis 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.Item An efficient approach for solving differential equations in the frame of a new fractional derivative operator(MDPI, 2023) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader; la Sen, Manuel De; Bayram, MustafaRecently, a new fractional derivative operator has been introduced so that it presents the combination of the Riemann–Liouville integral and Caputo derivative. This paper aims to enhance the reproducing kernel Hilbert space method (RKHSM, for short) for solving certain fractional differential equations involving this new derivative. This is the first time that the application of the RKHSM is employed for solving some differential equations with the new operator. We illustrate the convergence analysis of the applicability and reliability of the suggested approaches. The results confirm that the RKHSM finds the true solution. Additionally, these numerical results indicate the effectiveness of the proposed methodItem A novel method for fractal-fractional differential equations(Elsevier, 2022) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader; Asad, JihadWe consider the reproducing kernel Hilbert space method to construct numerical solutions for some basic fractional ordinary differential equations (FODEs) under fractal fractional derivative with the generalized Mittag–Leffler (M-L) kernel. Deriving the analytic and numerical solutions of this new class of differential equations are modern trends. To apply this method, we use reproducing kernel theory and two important Hilbert spaces. We provide three problems to illustrate our main results including the profiles of different representative approximate solutions. The computational results are compared with the exact solutions. The results obtained clearly show the effect of the fractal fractional derivative with the M-L kernel in the obtained outcomes. Meanwhile, the compatibility between the approximate and exact solutions confirms the applicability and superior performance of the methodItem 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 Local bifurcation analysis of one parameter in the greitzer’s model with a general compressor characteristic(Springer, 2022) Naima Meskine, Naima; Kessal, Mohand; Seba, DjamilaBased on the Greitzer’s reduced model, an analytical study on the instabilities phenomena of the operating point is presented using some basic properties of the nonlinear dynamic system. Moreover, a proposal of a general compressor characteristic curve, that suits the stationary system, is given. The Routh–Hurwitz theorem is applied to determine the stability conditions on the model parameters. An analysis along with a discussion is presented when the compression system goes to the Hopf bifurcation point during surge. For the Hopf bifurcation case, an approximate expression, for the periodic cycle of the system’s solution from the equilibrium point, is obtained and the direction is determined using Lyapunov’s stability theory. A numerical simulation is executed to illustrate the theoretical resultsItem Neighbourhood star selection properties in bitopological spaces(University of Nis, 2021) Lakehal, Rachid; Kočinac, Ljubiˇsa D.R.; Seba, DjamilaIn this paper we introduce and study some new types of star-selection principles ((i, j)-NSM, (i, j)-NSR and (i, j)-NSH) in bitopologivcal spaces. Various properties of these selection properties are established and their relations with known selection principles are discussed. Several examples are givenItem Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses(Elsevier, 2021) Boudjerida, Assia; Seba, DjamilaThis 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 resultItem Numerical solutions to the time-fractional swift–hohenberg equation using reproducing kernel hilbert space method(Springer, 2021) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, AbdelkaderIn this work, a numerical approach based on the reproducing kernel theory is presented for solving the fractional Swift–Hohenberg equation (FS-HE) under the Caputo time-fractional derivative. Such equation is an effective model to describe a variety of phenomena in physics. The analytic and approximate solutions of FS-HE in the absence and presence of dispersive terms have been described by applying the reproducing kernel Hilbert space method (RKHSM). The benefit of the proposed method is its ability to get the approximate solution of the FS-HE easily and quickly. The current approach utilizes reproducing kernel theory, some valuable Hilbert spaces, and a normal basis. The theoretical applicability of the RKHSM is demonstrated by providing the convergence analysis. By testing some examples, we demonstrated the potentiality, validity, and effectiveness of the RKHSM. The computational results are compared with other available ones. These results indicate the superiority and accuracy of the proposed method in solving complex problems arising in widespread fields of technology and scienceItem Numerical solution of the fractional relaxation-oscillation equation by using reproducing kernel hilbert space method(Springer, 2021) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, AbdelkaderIn this article, the reproducing kernel Hilbert space is proposed and analyzed for the relaxation-oscillation equation of fractional order (FROE). The relaxation oscillation is a type of oscillator based on the way that the physical system’s returns to its equilibrium after being disturbed. We make use of the Caputo fractional derivative. The approximate solution can be obtained by taking n-terms of the analytical solution that is in term of series formula. The numerical experiments are used to prove the convergence of the approximate solution to the analytical solution. The results obtained by the given method demonstrate that it is convenient and efficient for FROE