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

On a subdiffusive tumour growth model with fractional time derivative