Aging and Rejuvenation with Fractional Derivatives Metadata
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- Main Title Aging and Rejuvenation with Fractional Derivatives
Author: Aquino, GerardoCreator Type: PersonalCreator Info: University of North Texas
Author: Bologna, MauroCreator Type: PersonalCreator Info: University of North Texas
Author: Grigolini, PaoloCreator Type: PersonalCreator Info: University of North Texas; Universitá di Pisa and INFM; Istituto dei Processi Chimico Fisici del CNR
Author: West, Bruce J.Creator Type: PersonalCreator Info: United States. Army Research Office
Name: American Physical SocietyPlace of Publication: [College Park, Maryland]
- Creation: 2004-09-10
- Content Description: This article discusses aging rejuvenation with fractional derivatives.
- Physical Description: 11 p.
- Keyword: fractional derivatives
- Keyword: non-Poisson
- Journal: Physical Review E, 2004, College Park: American Physical Society 70:3
- Publication Title: Physical Review E
- Volume: 70
- Issue: 3
- Peer Reviewed: True
Name: UNT Scholarly WorksCode: UNTSW
Name: UNT College of Arts and SciencesCode: UNTCAS
- Rights Access: public
- DOI: 10.1103/PhysRevE.70.036105
- Archival Resource Key: ark:/67531/metadc67638
- Academic Department: Physics
- Academic Department: Center for Nonlinear Science
- Display Note: Copyright 2004 American Physical Society. The following article appeared in Physical Review E 70, 70:3; http://pre.aps.org/abstract/PRE/v70/i3/e036105
- Display Note: Abstract: We discuss a dynamic procedure that makes a fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index μ in the interval 2<μ<3, yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, o, is given by o=3-μ. A brand new system is characterized by the degree o=μ-2. If the system is prepared at time -tₐ<0 and the observation begins at time t=0, we derive the following scenario. For times 0<t«tₐ the system is satisfactorily described by the fractional derivative with o=3-μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t⪢tₐ yields o=μ-2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.