A numerical approach for solving the Fractal ordinary differential equations

In this paper, fractal differential equations are solved numerically. Here, the typical fractal equation is considered as follows:$$\frac{du(t)}{dt^{\alpha}}=f\left\{ t,u(t)\right\},~~~\alpha>0,$$ $f$ can be a nonlinear function and the main goal is to get $u(t)$. The continuous and discrete modes of this method have differences, so the subject must be carefully studied. How to solve fractal equations in their discrete form will be another goal of this research and also its generalization to higher dimensions than other aspects of this research.