Numerical solution for a fractional operator-based mathematical model of a brain tumour

Intricate mathematical models of malignant growths have been devised, particularly for solid tumours, whose growth is predominantly driven by cellular proliferation. The most severe type of brain cancer, gliomas, are distinguished by their extensive infiltration into nearby tissue. Glioma tumour growth is more aggressive than other types of cancer growth because of the diffusive behaviour of gliomas. The invasiveness of gliomas, however, necessitates a revision to incorporate cellular motility in addition to proliferative development. We examine some recent advances in the mathematical modelling of gliomas, and this study highlights how mathematical modelling can be used to create better glioblastoma multiforme (GBM) treatments. A simple two-dimensional mathematical model of glioma development and dissemination obtained from the fractional operator in terms of Caputo is the fractional Burgess equations (FBEs), which are expanded in this model. A newly introduced numerical algorithm based on an operational matrix extracted from the Taylor wavelets is described to find a solution for this model. This efficient numerical method transformed the given problem into a collection of algebraic equations. On solving these algebraic equations, we obtained the unknown coefficients. We found the solution to the given equation by substituting the unknown coefficients. Finally, three types of FBEs are used to simulate and test the suggested technique to verify its accuracy and superiority.