Complexity and the Fractional Calculus

Pensri Pramukkul; Adam Svenkeson; Paolo Grigolini; Mauro Bologna; Bruce West

doi:10.1155/2013/498789

journal article Open Access Jan 01, 2013

Complexity and the Fractional Calculus

Pensri Pramukkul Adam Svenkeson Paolo Grigolini

Mauro Bologna Bruce West

Advances in Mathematical Physics Vol. 2013 pp. 1-7 · Wiley

View at Publisher Save 10.1155/2013/498789

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.

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Metrics

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Citations

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References

Details

Published: Jan 01, 2013
Vol/Issue: 2013
Pages: 1-7
License: View

Authors

P

Pensri Pramukkul

Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427, USA

A

Adam Svenkeson

Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427, USA

P

Paolo Grigolini

Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427, USA

M

Mauro Bologna

Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 6-D, Arica, Chile

B

Bruce West

Information Science Directorate, Army Research Office, Research Triangle Park, NC 27709, USA

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

Complexity and the Fractional Calculus

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