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• W2783007365 abstract "Singular functions and, in general, Holder functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocity as a tool to characterize Holder and in particular singular functions. Fractional velocities are defined as limit of the difference quotient of a fractional power and they generalize the local notion of a derivative. On the other hand, their properties contrast some of the usual properties of derivatives. One of the most peculiar properties of these operators is that the set of their non trivial values is disconnected. This can be used for example to model instantaneous interactions, for example Langevin dynamics. Examples are given by the De Rham and Neidinger's functions, represented by iterative function systems. Finally the conditions for equivalence with the Kolwankar-Gangal local fractional derivative are investigated." @default.
• W2783007365 created "2018-01-26" @default.
• W2783007365 creator A5010053128 @default.
• W2783007365 date "2018-01-17" @default.
• W2783007365 modified "2023-10-13" @default.
• W2783007365 title "Fractional Velocity as a Tool for the Study of Non-Linear Problems" @default.
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• W2783007365 doi "https://doi.org/10.3390/fractalfract2010004" @default.
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