Reproducing kernel Hilbert space method for the numerical solutions of fractional cancer tumor models. (13th October 2020) - Attia, Nourhane; Akgül, Ali; Seba, Djamila; Nour, Abdelkader
Abstract : 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.