In this paper, we introduce neural networks as a method for solving fractal order differential equations. We delve into the concept of fractal derivatives on the Hausdorff metric and extend it to higher orders. Our network construction incorporates boundary conditions using linear Lagrange interpolation, ensuring that the output of the network satisfies the required constraints. The results show the ability of the network to approximate solutions with different dimensions of the fractal space \(\alpha \) and highlight the importance of the size of the network and the learning rate for the convection-diffusion equation, the Bessels equation, and the Burgers equation on the fractal medium.