Rhapsody in fractional

Abstract

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.

Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise

“…Thus, many researchers devote themselves to the theoretical analysis and practical application of fractional calculus. A rich variety of excellent books, review articles, papers and monographs dealing with fractional calculus and its application are available [4,[8][9][10][11][12][13][14][15][16][17][18].…”

Dynamics of theN-link pendulum: a fractional perspective

“…In this subsection, we recall a reliable method for computing A p , p ∈ C, based on the eigenvalue decomposition (Machado, Lopes, Duarte, Ortigueira, & Rato, 2014).…”

Fractional Jensen–Shannon Analysis of the Scientific Output of Researchers in Fractional Calculus

“…However, it was only in the last decades that FC was recognized as playing an important role in modeling and control of many important physical phenomena, and emerged as a key tool in the area of dynamical systems. Nowadays, the FC community is composed of many researchers in different scientific fields, namely, mathematics, physics, biology, finance and geophysics [36][37][38][39][40][41].…”