  In this paper, a free boundary problem modelling the growth of tumor is
considered. The model includes two reaction-diffusion equations modelling the
diffusion of nutrient and drug in the tumor and three hyperbolic equations
describing the evolution of three types of cells (i.e. proliferative cells,
quiescent cells and dead cells) considered in the tumor. Due to the fact that
in the real situation, the subdiffusion of nutrient and drug in the tumor can
be found, we have changed the reaction-diffusion equations to the fractional
ones to consider other conditions and study a more general and reliable model
of tumor growth. Since it is important to solve a problem to have a clear
vision of the dynamic of tumor growth under the effect of the nutrient and
drug, we have solved the fractional free boundary problem. We have solved the
fractional parabolic equations employing a combination of spectral and finite
difference methods and the hyperbolic equations are solved using characteristic
equation and finite difference method. It is proved that the presented method
is unconditionally convergent and stable to be sure that we have a correct
vision of tumor growth dynamic. Finally, by presenting some numerical examples
and showing the results, the theoretical statements are justified.
