AUTHOR=Manimaran J. , Shangerganesh L. , Debbouche Amar , Antonov Valery TITLE=Numerical Solutions for Time-Fractional Cancer Invasion System With Nonlocal Diffusion JOURNAL=Frontiers in Physics VOLUME=7 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00093 DOI=10.3389/fphy.2019.00093 ISSN=2296-424X ABSTRACT=

This article studies the existence and uniqueness of a weak solution of the time-fractional cancer invasion system with nonlocal diffusion operator. Existence and uniqueness results are ensured by adapting the Faedo-Galerkin method and some a priori estimates. Further, finite element numerical scheme is implemented for the considered system. Finally, various numerical computations are performed along with the convergence analysis of the scheme.