Publications Internationales

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

Browse

Has files: NoSubject: search.filters.subject.Gram–Schmidt orthogonalization process

Search Results

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    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.
  • No Thumbnail Available
    Item
    On solutions of time‐fractional advection–diffusion equation
    (WILEY ONLINE Library, 2020) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader
    In this paper, we present an attractive reliable numerical approach to find an approximate solution of the time‐fractional advection–diffusion equation (FADE) under the Atangana–Baleanu derivative in Caputo sense (ABC) with Mittag–Leffler kernel. The analytic and approximate solutions of FADE have been determined 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 solution of the FADE. Our main tools are reproducing kernel theory, some important Hilbert spaces, and a normal basis. The convergence analysis of the RKHSM is studied. The computational results are compared with other results of an appropriate iterative scheme and also by using specific examples, these results clearly show: On the one hand, the effect of the ABC‐fractional derivative with the Mittag–Leffler kernel in the obtained outcomes, and on the other hand, the superior performance of the RKHSM. From a numerical viewpoint, the RKHSM provides the solution's representation in a convergent series. Furthermore, the obtained results elucidate that the proposed approach gives highly accurate outcomes. It is worthy to observe that the numerical results of the specific examples show the efficiency and convenience of the RKHSM for dealing with various fractional problems emerging in the physical environment.