Dynamical and computational analysis of fractional order model of brain tumour growth

A fractional calculus-based model has been used in this work to study the growth and spreading of the most lethal forms of tumour, that is, glioblastomas, via incorporating two important factors, namely intercellular cell invasion via diffusion and cell proliferation. As nonlocal fractional derivatives possess an inherent memory-preserving quality, the suggested model produces the most relevant results. The model is constructed using the fractional-order Burgers’ equation to correctly demonstrate the invasive characteristics of gliomas and solutions have been obtained using effective and powerful analytical methods. We employed the q-homotopy analysis generalized transform method (q-HAGTM) and the generalized Laplace decomposition method (GLDM) to derive an approximate analytical solution for the studied model. Non-integer derivatives have been used in the model instead of classical derivatives, and classical solution has been obtained as a special case. Finally, we discussed the effect of this model in predicting the growth rate and effect of treatment on gliomas with the help of simulations and graphical representations. This approach enables us to comprehend these diseases and has the potential to develop efficient and effective methods for their treatment and cure.