Regularization of derivatives on non-differentiable points. (March 2016) - Prodanov, Dimiter
Abstract: The notion of derivative is limited only to the idealization of linear growth. The paper presents a formal regularization procedure for the derivatives of functions using the fractional velocity, i.e. a local fractional derivation operation. The approach can be applied in strongly non-linear or fractal settings, such as singular functions, Brownian motion, quantum paths, etc.