Complexity and the fractional calculus
type: Item
instance of: scholarly article
title: Complexity and the fractional calculus
zbMATH Open document ID: 1276.60027
DOI: 10.1155/2013/498789
author: Pensri Pramukkul
author: Adam Svenkeson
author: Paolo Grigolini
author: Mauro Bologna
author: Bruce J. West
published in: Advances in Mathematical Physics
publication date: 2013-06-07T00:00:00Z
review text: Summary: We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories each of which satisfies the stochastic central limit theorem and the condition for Mittag-Leffler universality.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G07
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6171638
Wikidata QID: Q58918850
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/498789
OpenAlex ID: W2128614559
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description: scientific article; zbMATH DE number 6171638