### Abstract

The normal way of introducing the notion of derivative is by means of the limit of an incremental ratio that can assume three forms, depending the used translations as we saw in Chaps. 1 and 4. On the other hand, in those derivatives the limit operation is done over a set of points uniformly spaced: a linear scale was used. Here we present an alternative derivative, that is valid only for t > 0 or t < 0 and uses an exponential scale

Original language | Unknown |
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Title of host publication | Fractional Calculus for Scientists and Engineers |

Place of Publication | Berlin |

Publisher | Springer-Verlag |

Pages | 123-144 |

Volume | 84 |

ISBN (Print) | 978-94-007-0747-4 |

DOIs | |

Publication status | Published - 1 Jan 2011 |

### Publication series

Name | Lecture Notes in Electrical Engineering |
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Publisher | Springer-Verlag |

ISSN (Print) | 1876-1100 |

## Cite this

Ortigueira, M. D., & DEE Group Author (2011). The Fractional Quantum Derivative and the Fractional Linear Scale Invariant Systems. In

*Fractional Calculus for Scientists and Engineers*(Vol. 84, pp. 123-144). (Lecture Notes in Electrical Engineering). Springer-Verlag. https://doi.org/10.1007/978-94-007-0747-4_6