Publications Internationales

Permanent URI for this collectionhttps://dspace.univ-boumerdes.dz/handle/123456789/13

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Author: search.filters.author.Seba, DjamilaSubject: search.filters.subject.Caputo derivative

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    Numerical solution of the fractional relaxation-oscillation equation by using reproducing kernel hilbert space method
    (Springer, 2021) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader
    In 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
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    Solving Duffing-Van der Pol Oscillator Equations of Fractional Order by an Accurate Technique
    (Shahid Chamran University of Ahvaz, 2021) Attia, Nourhane; Seba, Djamila; Akgül, Ali; Nour, Abdelkader
    In this paper, an accurate technique is used to find an approximate solution to the fractional-order Duffing-Van der Pol (DVP, for short) oscillators equation which is reproducing kernel Hilbert space (RKHS, for short ) method. The numerical results show that the n-term approximation is a rapidly convergent series representation and they present also the high accuracy and effectiveness of this method. The efficiency of the proposed method has been proved by the theoretical predictions and confirmed by the numerical experiments