Publications Scientifiques
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Item 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 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, HamzaThis 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 exampleItem Reproducing kernel Hilbert space method for the numerical solutions of fractional cancer tumor models(2020) Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, AbdelkaderThis 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.Item On the application of measure of noncompactness to the existence of solutions for fractional differential equations(Springer, 2009) Agarwal, Ravi P.; Benchohra, Mouffak; Seba, DjamilaItem Measure of noncompactness and hyperbolic partial fractional differential equations in banach spaces(2010) Benchohra, M.; Nieto, J.J.; Seba, Djamila