On Fractal Derivatives and Applications

In this paper, we develop some fundamental tools for fractal derivatives, such as a Leibniz‐type product rule and a chain rule. Also, a local Picard theorem for an initial value problem via fractal derivatives is obtained. Finally, the Gompertz and logistic models associated to those differential operators are considered. We also show how effective these models are compared to other well‐known (classical and conformable) models when applied to an example of real data.