  In this work, we present and analyse a system of coupled partial differential
equations, which models tumour growth under the influence of subdiffusion,
mechanical effects, nutrient supply, and chemotherapy. The subdiffusion of the
system is modelled by a time fractional derivative in the equation governing
the volume fraction of the tumour cells. The mass densities of the nutrients
and the chemotherapeutic agents are modelled by reaction diffusion equations.
We prove the existence and uniqueness of a weak solution to the model via the
Faedo--Galerkin method and the application of appropriate compactness theorems.
Lastly, we propose a fully discretised system and illustrate the effects of the
fractional derivative and the influence of the fractional parameter in
numerical examples.
