Rhapsody in fractional

Machado, J. A. Tenreiro; Lopes, António M.; Duarte, Fernando B.; Ortigueira, Manuel D.; Rato, Raul T.

http://hdl.handle.net/10400.22/5496

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Authors

Machado, J. A. Tenreiro

Lopes, António M.

Duarte, Fernando B.

Ortigueira, Manuel D.

Rato, Raul T.

Abstract(s)

This paper studies several topics related with the concept of “fractional” 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 probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Keywords

Positional number systems Fractional sums Matrix power Matrix root Tolerant computing Negative probability Fractional delay Difference equations Fractional Fourier transform