Generalization of the classical derivative function at a point and its application

Abstract

In the paper one generalization of the derivative is considered which in some cases simplifies the study of a function on differentiability, nowhere differentiability, singularity, in particular, the differentiability of the Weierstrass’s function is studied, provided that ???????? < 1 and ???? ≥ 3. Also, the application of the obtained results to the disclosure of some uncertainties is considered.