Publications Internationales

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

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Author: search.filters.author.Attia, NourhaneSubject: search.filters.subject.Caputo fractional derivative

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    Numerical solutions to the time-fractional swift–hohenberg equation using reproducing kernel hilbert space method
    (Springer, 2021) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader
    In 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 science
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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.