Abstract
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.
Topics

No keywords indexed for this article. Browse by subject →

Cited By
41
Fractional Dynamics of Individuals in Complex Networks

Malgorzata Turalska, Bruce J. West · 2018

Frontiers in Physics
Metrics
41
Citations
38
References
Details
Published
Jan 01, 2013
Vol/Issue
2013
Pages
1-7
License
View
Funding
Welch Foundation Award: 1110231
ARO Award: 1110231
Fondo Nacional de Desarrollo Cientìfico y Tecnológico Award: 1110231
Cite This Article
Pensri Pramukkul, Adam Svenkeson, Paolo Grigolini, et al. (2013). Complexity and the Fractional Calculus. Advances in Mathematical Physics, 2013, 1-7. https://doi.org/10.1155/2013/498789