### Abstract

This paper studies several topics related with the concept of “frac- tional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabil- ities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Original language | English |
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Pages (from-to) | 1188-1214 |

Journal | Fractional Calculus and Applied Analysis |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- difference equations
- fractional delay
- fractional Fourier transform
- fractional sums
- matrix power
- matrix root
- negative probability
- positional number systems
- tolerant computing

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## Cite this

Machado, J. T., Lopes, A. M., Duarte, F. B. M., Ortigueira, M. D., & Rato, R. T. (2014). Rhapsody in fractional.

*Fractional Calculus and Applied Analysis*,*17*(4), 1188-1214. https://doi.org/10.2478/s13540-014-0206-0