Quantum derivatives and the Schrödinger equation
The authors justify the results of [\textit{L. Nottale} Astronom Asrophys. 327, 867--889 (1997), Chaos Solutions Fractals 10, No. 2--3, 459--468 (1999; Zbl 0997.81526)]. The authors give a precise definition of scale derivatives by means of quantum derivatives for non-differentiable functions. Note that these derivatives are not derivations on the set of continuous functions, since they do not satisfy the Leibniz rule. It is shown that scale derivation is an extension of ordinary differentiation. It is derived the Schrödinger equation via the scale-relativity principle and Newton's fundamental equation of dynamics.
scientific article; zbMATH DE number 2093082