Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus

This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences similarities. The derivative is closely connected to Haussdorff's concepts dimension geometry. paper distinguishes between the a function on domain function, where image space. Different continuous approximations for are discussed, it shown that $q$-calculus approximation function. A similar version can be obtained Caputo's also proportional derivative, corresponding leads Caputo-like derivative. has implications studies differential equations, anomalous diffusion, information epidemic spread in systems,