Aging and Rejuvenation with Fractional Derivatives


This article discusses aging rejuvenation with fractional derivatives.

Creation Date: September 10, 2004
UNT College of Arts and Sciences
UNT Scholarly Works
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Creator (Author):
Aquino, Gerardo

University of North Texas

Creator (Author):
Bologna, Mauro

University of North Texas

Creator (Author):
Grigolini, Paolo

University of North Texas; Universitá di Pisa and INFM; Istituto dei Processi Chimico Fisici del CNR

Creator (Author):
West, Bruce J.

United States. Army Research Office

Publisher Info:
Publisher Name: American Physical Society
Place of Publication: [College Park, Maryland]
  • Creation: September 10, 2004

This article discusses aging rejuvenation with fractional derivatives.

Department: Physics

Copyright 2004 American Physical Society. The following article appeared in Physical Review E 70, 70:3;


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.

Physical Description:

11 p.

Keyword(s): fractional derivatives | non-Poisson
Source: Physical Review E, 2004, College Park: American Physical Society 70:3
UNT College of Arts and Sciences
UNT Scholarly Works
  • DOI: 10.1103/PhysRevE.70.036105 |
  • ARK: ark:/67531/metadc67638
Resource Type: Article
Format: Text
Access: Public
Publication Title: Physical Review E
Volume: 70
Issue: 3
Peer Reviewed: Yes