Complexity and the Fractional Calculus
| Autor: | Mauro Bologna, Adam Svenkeson, Paolo Grigolini, Pensri Pramukkul, Bruce J. West |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
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Article Subject
Differential equation Stochastic process Applied Mathematics Physics QC1-999 Mathematical analysis General Physics and Astronomy Malliavin calculus Fractional calculus Universality (dynamical systems) Applied mathematics Ergodic theory Universal property Central limit theorem Mathematics |
| Zdroj: | ADVANCES IN MATHEMATICAL PHYSICS Artículos CONICYT CONICYT Chile instacron:CONICYT Advances in Mathematical Physics, Vol 2013 (2013) |
| ISSN: | 1687-9120 |
| 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: | OpenAIRE |
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