This research introduces a novel mathematical model for brain tumor growth incorporating a fractal fractional derivative. We investigate the existence and uniqueness of solutions for this model, as well as its stability properties, using a novel contraction known as the generalized $\alpha-\psi$-Geraghty-type contraction. Our stability analysis is based on the Ulam–Hyers framework. The findings presented in this study constitute a significant contribution to the field.
