Regularization of derivatives on non-differentiable points

Emergent Quantum Mechanics 2015

Prodanov, Dimiter^1

Department of Environment, Health and Safety, Neuroscience Research Flanders, Imec, Leuven, Belgium^1

关键词: Fractional derivations;    Linear growth;    Non linear;    Non-differentiable points;    Regularization procedure;    Singular functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/701/1/012031/pdf
DOI  :  10.1088/1742-6596/701/1/012031

来源: IOP

【 摘 要 】

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.