Complexity and the Fractional Calculus

Autor: Pensri Pramukkul, Adam Svenkeson, Paolo Grigolini, Mauro Bologna, Bruce West
Jazyk: angličtina
Rok vydání: 2013
Předmět:
Zdroj: Advances in Mathematical Physics, Vol 2013 (2013)
Druh dokumentu: article
ISSN: 1687-9120
1687-9139
DOI: 10.1155/2013/498789
Popis: 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 the Mittag-Leffler universality.
Databáze: Directory of Open Access Journals
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