Mathematical analysis of a time-fractional coupled tumour model using Laplace and finite Fourier transforms

A time-fractional diffusive tumour growth model is investigated in this paper. The model assumes two different tumour populations having diverse diffusion and proliferation rates. The classical integer model, coupled with the fractional operators with power-law, Mittag-Leffler and exponential kernels is solved analytically with the help of integral transforms Numerical investigations of the resulting solution are carried out to examine the effect of the different fractional operators. The spherical form of the model is considered, as this describes the tumour more adequately as compared to other coordinates system. From the numerical experiments, it is observed that, the kernel contained in the respective fractional operator could alter the dynamics of the tumour concentration under consideration.